some convergence theorems of the mann iteration for monotone α nonexpansive mappings in this paper we introduce the concept of monotone nonexpansive mappings in an ordered banach space e with the partial order which contains monotone nonexpansive mappings as special case with the help of the mann iteration we show some existence theorems of fixed points of monotone nonexpansive mappings in uniformly convex ordered banach space also we prove some weak and strong convergence theorems of the mann iteration for finding an order fixed point of monotone nonexpansive mappings under the condition lim sup n n 1 n 0 or lim inf n n 1 n 0

convergence and stability of iterative algorithms of generalized set valued variational like inclusions in banach spaces abstract in this paper we give the notion of p proximal mapping an extension of p proximal mapping given by ding and xia j comput appl math 147 2002 369 for a nonconvex lower semicontinuous subdifferentiable proper functional on banach space and prove its existence and lipschitz continuity further we consider a class of generalized set valued variational like inclusions in banach space and show its equivalence with a class of implicit wiener hopf equations using the concept of p proximal mapping using this equivalence we propose a new class of iterative algorithms for the class of generalized set valued variational like inclusions furthermore we prove the existence of solution of generalized set valued variational like inclusions and discuss the convergence criteria and the stability of the iterative algorithm

new perturbed finite step iterative algorithms for a system of extended generalized nonlinear mixed quasi variational inclusions this paper introduces a new system of extended generalized nonlinear mixed quasi variational inclusions involving a maximal m relaxed h accretive so called a h accretive lan et al 2006 37 mappings in q uniformly smooth banach spaces by using the resolvent operator technique for a maximal m relaxed h accretive mappings due to lan et al we establish the existence and uniqueness of solution for this system of extended generalized nonlinear mixed quasi variational inclusions and construct a new perturbed n step iterative algorithm with mixed errors for solving the mentioned system we also prove the convergence of the sequences generated by our algorithms in q uniformly smooth banach spaces the results presented in this paper extend and improve some known results in the literature

strong convergence for the modified mann s iteration of λ strict pseudocontraction abstract in this paper for an strict pseudocontraction t we prove strong convergence of the modified mann s iteration defined by x n 1 n u n x n 1 n n n tx n 1 n x n where n n and n in 0 1 satisfy i 0 n k 2 with lim inf n n k 2 n 0 ii lim n n 0 and n 1 n iii lim sup n n 1 our results unify and improve some existing results

existence of uncountably many bounded nonoscillatory solutions and their iterative approximations for second order nonlinear neutral delay difference equations in this paper the banach fixed point theorem is employed to establish several existence results of uncountably many bounded nonoscillatory solutions for the second order nonlinear neutral delay difference email protected n dx n b n x email protected email protected n x h 1 n x h 2 n x h k n f n x f 1 n x f 2 n x f k n c n n n 0 where t email protected n n email protected n 0 a b c n n 0 r with a n 0 for email protected n n 0 h f n n 0xr k r and h l f l n n 0 z withlimn h l n limn f l n email protected 1 2 k a few mann type iterative approximation schemes with errors are suggested and the errors estimates between the iterative approximations and the nonoscillatory solutions are discussed seven nontrivial examples are given to illustrate the advantages of our results

the solution by iteration of nonlinear equations involving psi strongly accretive operators let e be an arbitrary real banach space and let k c e be a proximal subset of e suppose t k i e is a lipschitz strongly accretive operator such that for any given g e the equation tx f has a solution x e d t it is proved that modified iteration processes of the mann and ishikawa types converge strongly to x related results deal with the solution of the equation x tx f 0 for a strongly accretive or strongly dissipative t and the iterative approximation of fixed points to a strongly pseudocontractive t we also discuss the case where the operator t is only uniformly continuous miramare trieste december 1996 permanent address department of mathematics and computer science nnamdi azikiwe university p m b 5025 awka anambra state nigeria

strong convergence of iterative methods for k strictly pseudo contractive mappings in hilbert spaces in this paper we introduce composite iterative schemes for finding fixed points of k strictly pseudo contractive mappings for some 0

iterative process with errors of nonlinear equations involvingm accretive operators abstract let x be a uniformly smooth and uniformly convex banach space and t d t x x be an m accretive operator with the domain d t and the range r t for any given f x we prove that the mann and ishikawa type iterative sequences with errors converge strongly to the unique solution of the equation x tx f where t may not be lipschitz some related results deal with the convergence of mann and ishikawa type iterative sequences with errors for approximating a solution of a continuous dissipative operator equation

convergence theorems by a new iteration process for a finite family of nonself asymptotically nonexpansive mappings with errors in banach spaces in this paper we study a new iteration process for a finite family of nonself asymptotically nonexpansive mappings with errors in banach spaces we prove some weak and strong convergence theorems for this new iteration process the results of this paper improve and extend the corresponding results of chidume et al 2003 10 osilike and aniagbosor 2000 3 schu 1991 4 takahashi and kim 1998 9 tian et al 2007 18 wang 2006 11 yang 2007 17 and others

approximating fixed points of φ hemicontractive mappings by the ishikawa iteration process with errors in uniformly smooth banach spaces abstract let e be a uniformly smooth banach space and t e e be a continuous and strongly o hemicontractive mapping this paper proves that under suitable conditions the ishikawa iterative sequence with errors strongly converges to the unique fixed point of t the related result deals with the strong convergence of the ishikawa iterative sequence with errors to the unique solution of the equation t x f when t e e is o strongly accretive these results generalize the results of ding 1 into more general o hemicontractive operators and extend a recent paper written by osilike 2 in two ways 1 i the lipschitzian continuity is replaced by the continuity on mapping t 2 ii if the errors u n v n 0 for all n n our theorems of this paper extend results of osilike 2 to the more general class of real uniformly smooth banach spaces

iterative processes with mixed errors for nonlinear equations with perturbed m accretive operators in banach spaces let x be a real uniformly smooth banach space of which the dual x has a frechet differentiable norm let a d a x 2 x be an m accretive operator with closed domain d a and bounded range r a and s x x a continuous and a strongly accretive operator with bounded range r i s it is proved that the ishikawa and mann iterative processes with mixed errors converge strongly to the unique solution of the equation z sx lax for given z x and l 0

mann and ishikawa iterations with errors for asymptotically nonexpansive mappings abstract in a recent paper rhoades 1 presented some generalizations of schu 2 on the convergence of the mann and ishikawa iterations of asymptotically nonexpansive mappings in uniformly convex banach spaces we continue the study on the ishikawa and mann iteration process with errors and prove that if x is a uniformly convex banach space o e x closed bounded and convex and t e e is an asymptotically nonexpansive mapping then the ishikawa and mann iteration process with errors converges strongly to some fixed point of t

convergence and certain control conditions for hybrid iterative algorithms very recently yao et al 2010 4 proposed a hybrid iterative algorithm under the parameter sequences satisfying some quite restrictive conditions they derived a strong convergence theorem in a hilbert space in this paper under the weaker conditions we prove the strong convergence of the sequence generated by their iterative algorithm to a common fixed point of an infinite family of nonexpansive mappings which solves a variational inequality an appropriate example such that all conditions of this result that are satisfied and that other conditions are not satisfied is provided moreover the method of our paper is different from the method in yao et al 2010 4

analyticity of hybrid systems arising in visco and thermo elastic structures abstract we consider two systems arising in a two dimensional viscoelastic fluid structure interaction one of them coupled with a wave equation with interior damping of kelvin voigt type in the second model the acoustic vibrations of the viscous fluid which fills the two dimensional interior cavity are coupled with the mechanical vibrations of a one dimensional thermoelastic beam therefore the systems are related to the problem of the active control of noise in a cavity our main results are that the corresponding semigroups are analytic in particular we show the exponential stability of the models

convergence of iterative processes with errors for set valued pseudocontractive and accretive type mappings in banach spaces abstract in this paper some new results on convergence of iterative processes with errors for set valued pseudocontractive and accretive mappings in banach spaces are obtained our results extend and improve a number of the recent results

convergence and stability of perturbed three step iterative algorithm for completely generalized nonlinear quasivariational inequalities in this paper we introduce a new class of completely generalized nonlinear quasivariational inequalities and obtain its equivalence with a class of fixed point problems by using the resolvent operator technique using this equivalence we develop perturbed three step iterative algorithm for this class of completely generalized quasivariational inequalities we establish a few existence theorems of unique solution for the class of completely generalized quasivariational inequalities involving relaxed monotone generalized pseudocontractive and strongly monotone mappings and prove some convergence and stability results of iterative sequence generated by perturbed three step iterative algorithm

iterative solution of nonlinear equations involving set valued uniformly accretive operators abstract let e be a real normed linear space and let a e 2 e be a uniformly continuous and uniformly quasi accretive multivalued map with nonempty closed values such that the range of i a is bounded and the inclusion f ax has a solution x e it is proved that ishikawa and mann type iteration processes converge strongly to x further if t e 2 e is a uniformly continuous and uniformly hemicontractive set valued map with bounded range and a fixed point x e it is proved that both the mann and ishikawa type iteration processes converge strongly to x the strong convergence of these iteration processes with errors is also proved

nonlinear relaxed cocoercive variational inclusions involving a η accretive mappings in banach spaces in this paper we introduce a new concept of a h accretive mappings which generalizes the existing monotone or accretive operators we study some properties of a h accretive mappings and define resolvent operators associated with a h accretive mappings by using the new resolvent operator technique we also construct a new perturbed iterative algorithm with mixed errors for a class of nonlinear relaxed cocoercive variational inclusions involving a h accretive mappings and study applications of a h accretive mappings to the approximation solvability of this class of nonlinear relaxed cocoercive variational inclusions in q uniformly smooth banach spaces our results improve and generalize the corresponding results of recent works

on a mann type implicit iteration process for continuous pseudo contractive mappings abstract let k be a nonempty closed convex subset of a banach space e t k k a continuous pseudo contractive mapping suppose that n is a real sequence in 0 1 satisfying appropriate conditions then for arbitrary x 0 k the mann type implicit iteration process x n given by x n n x n 1 1 n t x n n 0 strongly and weakly converges to a fixed point of t respectively

approximating solutions for the systems of strongly accretive operator equations the purpose of this paper is to study a strong convergence of multi step iterative scheme to a common fixed point for a finite family of strongly pseudo contractive mappings as a consequence the strong convergence theorems for the modified multi step iterative sequence to a solution of systems of strongly accretive operator equations are obtained in real uniformly smooth banach spaces the results presented in this paper improve and extend the corresponding xu y xu ishikawa and mann iterative processes with errors for nonlinear strongly accretive operator equations j math anal appl 224 1998 91 101 and noor rassias and huang m a noor t m rassias z huang three step iterations for nonlinear accretive operator equations j math anal appl 274 2002 59 68 and many others

mann iteration of cesaro means for asymptotically non expansive mappings abstract let k be a nonempty closed convex subset of a uniformly convex banach space e with a uniformly g teaux differentiable norm suppose that t k k is an asymptotically non expansive mapping and for arbitrary initial value x 0 k we will introduce the mann iteration of its cesaro means x n 1 n x n 1 n 1 n 1 j 0 n t j x n n 0 and prove its strong and weak convergence whenever n 0 b n and n is a real sequence in 0 1 satisfying one of the conditions either i lim n n 0 or ii n 0 n 1 n or iii 0 lim inf n n lim sup n n 1

a note on stevic s iteration method abstract in the present paper motivated by stevic s iteration method we show the stability result of the following unified iterative scheme x n 1 t n t v n 1 t n x n u n for a strongly pseudocontractive selfmapping t this stability result implies the stability of stevic s iteration scheme naturally

strong convergence of an explicit iterative algorithm for continuous pseudo contractions in banach spaces let c be a nonempty closed convex subset of a real banach space x whose norm is uniformly g teaux differentiable and t c c be a continuous pseudo contraction with a nonempty fixed point set f t for arbitrary given element u c and for t 0 1 let yt be the unique continuous path such that yt 1 t tyt tu assume that yt p f t as t 0 let n n and n be three real sequences in 0 1 satisfying the following conditions i n n n 1 ii limn n limn n 0 iii limn n1 n 0 or iii n 0 n1 n let n be a summable sequence of positive numbers for arbitrary initial datum x0 x00 c and a fixed n 0 construct elements xnm as follows xnm 1 nu nxn ntxnm m 0 1 2 suppose that there exists a least positive integer n n satisfying the following condition txnn n 1 txnn n n 1 1 n n define iteratively a sequence xn in an explicit manner as follows xn 1 xn 10 xnn n 1 nu nxn ntxnn n n 0 then xn converges strongly to a fixed point of t for all the continuous pseudo contractive mappings for which is possible to construct the sequence xn this result improves and extends a recent result of yao et al yonghong yao yeong cheng liou rudong chen strong convergence of an iterative algorithm for pseudocontractive mapping in banach spaces nonlinear anal 67 2007 3311 3317

equivalence theorems of the convergence between ishikawa and mann iterations with errors for generalized strongly successively φ pseudocontractive mappings without lipschitzian assumptions abstract in this paper the equivalence of the strong convergence between the modified mann and ishikawa iterations with errors in two different schemes by xu y g xu ishikawa and mann iteration process with errors for nonlinear strongly accretive operator equations j math anal appl 224 1998 91 101 and liu l s liu ishikawa and mann iterative process with errors for nonlinear strongly accretive mappings in banach spaces j math anal appl 194 1995 114 125 respectively is proven for the generalized strongly successively pseudocontractive mappings without lipschitzian assumption our results generalize the recent results of the papers zhenyu huang f bu the equivalence between the convergence of ishikawa and mann iterations with errors for strongly successively pseudocontractive mappings without lipschitzian assumption j math anal appl 325 1 2007 586 594 b e rhoades s m soltuz the equivalence between the convergences of ishikawa and mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive maps j math anal appl 289 2004 266 278 b e rhoades s m soltuz the equivalence between mann ishikawa iterations and multi step iteration nonlinear anal 58 2004 219 228 by extending to the most general class of the generalized strongly successively pseudocontractive mappings and hence improve the corresponding results of all the references given in this paper by providing the equivalence of convergence between all of these iteration schemes for any initial points u 1 x 1 in uniformly smooth banach spaces

convergence and almost stability of ishikawa iterative scheme with errors for m accretive operators let x be a uniformly smooth real banach space and t x x be a generalized lipschitzian and m accretive operator it is proved that under suitable conditions the ishikawa iterative schemes with errors both converges strongly to the unique solution of the nonlinear operator equation x tx f and is almost stable a few related results deal with the operator equations for the dissipative type operator the results presented in this paper extend substantially the corresponding results in 1 2

convergence theorems for ψ expansive and accretive mappings abstract let e be a real banach space and let a d a e e be a lipschitz expansive and accretive mapping such that c o d a 0 r i a suppose that there exists x 0 d a where one of the following holds i there exists r 0 such that r 2 a x 0 or ii there exists a bounded neighborhood u of x 0 such that t x x 0 a x for x u d a and t 0 an iterative sequence x n is constructed to converge strongly to a zero of a related results deal with the strong convergence of this iteration process to fixed points of expansive and pseudocontractive mappings in real banach spaces the convergence results established in this paper are new for this more general class of expansive and accretive or pseudocontractive mappings

the solution by iteration of nonlinear equations in uniformly smooth banach spaces abstract letebe a uniformly smooth banach space and lett d t e ebe a strong pseudocontraction with an open domaind t ineand a fixed pointx d t we establish the strong convergence of the mann and ishikawa iterative processes with errors to the fixed point oft related results deal with the iterative solution of operator equations of the formsf txandf x tx 0 whentis a set valued strongly accretative operator our theorems include the cases in which the operatortis defined only locally explicit error estimates are also given

simpler is also better in approximating fixed points in this paper we demonstrate that a number of fixed point iteration problems can be solved using a modified krasnoselskij iteration process which is much simpler to use than the other iteration schemes that have been defined

strong convergence theorem for uniformly l lipschitzian asymptotically pseudocontractive mapping in real banach space abstract let e be a real banach space let k be a nonempty closed and convex subset of e t k k a uniformly l lipschitzian asymptotically pseudocontractive mapping with sequence k n n 0 1 lim n k n 1 such that f t let n n 0 0 1 be such that n 0 n n 0 n 2 and n 0 n k n 1 suppose x n n 0 is iteratively defined by x n 1 1 n x n n t n x n n 0 and suppose there exists a strictly increasing continuous function 0 0 0 0 such that t n x x j x x k n x x 2 x x x k it is proved that x n n 0 converges strongly to x f t it is also proved that the sequence of iteration x n defined by x n 1 a n x n b n t n x n c n u n n 0 where u n n 0 is a bounded sequence in k and a n n 0 b n n 0 c n n 0 are sequences in 0 1 satisfying appropriate conditions converges strongly to a fixed point of t

convergence of composite iterative methods for finding zeros of accretive operators abstract strong convergence theorems on composite iterative schemes by the viscosity approximation methods for finding a zero of an accretive operator are established in banach spaces the main results generalize the recent corresponding results of aoyama et al k aoyama y kimura w takahashi m toyoda approximation of common fixed points of a countable family of nonexpansive mappings in banach spaces nonlinear anal 67 2007 2350 2360 ceng et al l c ceng a r khan q h ansari j c yao strong convergence of composite iterative schemes for zeros of m accretive operators in banach spaces nonlinear anal 70 2009 1830 1840 kim and xu t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 2005 51 60 and xu h k xu strong convergence of an iterative method for nonexpansive and accretive operators j math anal appl 314 2006 631 643 to viscosity methods in a strictly convex and reflexive banach space having a uniformly g teaux differentiable norm our results also improve the corresponding results of t d benavides g l acedo h k xu iterative solutions for zeros of accretive operators math nachr 248 249 2003 62 71 r chen z zhu viscosity approximation fixed points for nonexpansive and m accretive operators fixed point theory appl 2006 2006 1 10 s kamimura w takahashi approximation solutions of maximal monotone operators in hilbert spaces j approx theory 106 2000 226 240 p e mainge viscosity methods for zeroes of accretive operators j approx theory 140 2 2006 127 140 k nakajo strong convergence to zeros of accretive operators in banach spaces j nonlinear convex anal 7 2006 71 81

iterative algorithms for a new class of extended general nonconvex set valued variational inequalities abstract some new classes of extended general nonconvex set valued variational inequalities and the extended general wiener hopf inclusions are introduced by the projection technique equivalence between the extended general nonconvex set valued variational inequalities and the fixed point problems as well as the extended general nonconvex wiener hopf inclusions is proved then by using this equivalent formulation we discuss the existence of solutions of the extended general nonconvex set valued variational inequalities and construct some new perturbed finite step projection iterative algorithms with mixed errors for approximating the solutions of the extended general nonconvex set valued variational inequalities we also verify that the approximate solutions obtained by our algorithms converge to the solutions of the extended general nonconvex set valued variational inequalities the results presented in this paper extend and improve some known results from the literature

existence and iterative approximations of nonoscillatory solutions of higher order nonlinear neutral delay differential equations this paper studies a few existence results of nonoscillatory solutions for the following higher order nonlinear neutral delay differential equation dndtnx t cx t 1 n i 1didtih t x h1 t x h2 t x hk t 1 n 1f t x f1 t x f2 t x fk t g t t t0 where n is a positive integer 0 i n 1 c r 1 0 h ci t0 rk r f c t0 rk r g c t0 r hl ci t0 r and fl c t0 r with limt hl t limt fl t l 1 k constructs several mann type iterative approximation sequences with errors for these nonoscillatory solutions and establish some error estimates between the approximate solutions and the nonoscillatory solutions in addition sufficient conditions for the existence of infinitely many nonoscillatory solutions for the above equation are given three nontrivial examples are given to illustrate the advantages of our results

mann and ishikawa iterations with errors for non lipschitzian mappings in banach spaces let c be a nonempty closed convex subset of a uniformly convex banach space and let t c c be completely continuous asymptotically nonexpansive in the intermediate sense in this paper we prove that the ishikawa and mann iteration process with errors converges strongly to some fixed point of t which generalizes the recent results due to huang 1

on generalized set valued variational inclusions abstract we point out a basic flaw made by m a noor 1998 j math anal appl 228 206 220 construct a new iterative algorithm for a class of variational inclusions involving non monotone set valued mappings with noncompact values and study the convergence of the perturbed ishikawa iterative process for solving a class of the generalized single valued variational inclusions

algorithms for zeros of two accretive operators for solving convex minimization problems and its application to image restoration problems abstract in this paper a new viscosity iterative method minimization algorithm for image restoration algorithm is proposed based on a new viscosity iteration the algorithm for finding the common zeros of two accretive operators in the framework of uniformly smooth banach spaces moreover the strong convergence theorems for the iterative algorithms and an example is proposed which shows the validity of main theorem are proved the results of this paper are improved and extended of the corresponding ones announced by many others and we also applied our result to solve a convex minimization problem and g teaux differentiable e p s and variational inequality experiment results show that the proposed algorithms outperform some other methods finally we give the numerical experiments to show the efficiency and advantage of the proposed methods and we also used our proposed algorithm for applying to solve the image deblurring and image recovery problems

existence and iterative approximation of solutions of generalized mixed equilibrium problems in this paper we consider a generalized mixed equilibrium problem involving non monotone set valued mappings in real hilbert space we extend the notions of the yosida approximation and its corresponding regularized operator given by moudafi and thera a moudafi m thera proximal and dynamical approaches to equilibrium problems in lecture notes in econom and math system vol 477 springer verlag berlin 2002 pp 187 201 and discuss some of their properties further we consider a generalized wiener hopf equation problem and show its equivalence with the generalized mixed equilibrium problem using a fixed point formulation of the generalized wiener hopf equation problem we construct an iterative algorithm furthermore we extend the notion of stability given by harder and hick a m harder t l hicks stability results for fixed point iteration procedures math japonica 33 5 1998 693 706 we prove the existence of a solution and discuss the convergence and stability of the iterative algorithm for the generalized wiener hopf equation problem since the generalized mixed equilibrium problems include variational inequalities as special cases the results presented in this paper continue to hold for these problems

convergence theorems for φ strongly accretive and φ hemicontractive operators suppose that x is an arbitrary real banach space and t x x is a continuous strongly accretive operator it is shown that the nonlinear equation tx f has a unique solution and under certain conditions both the mann and ishikawa iteration methods with errors introduced by y xu 1998 j math anal appl 224 91 101 converge strongly to the solution a related result deals with the approximation of fixed points of hemicontractive operators

halpern type proximal point algorithm of accretive operators abstract the main objectives of this paper are to employ a new proof technique to prove the strong convergence of x n and y n defined respectively by x n 1 n u n x n 1 n n j r n a x n and y n 1 n y n 1 n j r n a n u 1 n y n to some zero of accretive operator a in a uniformly convex banach space e with a uniformly g teaux differentiable norm or with a weakly continuous duality mapping j whenever n and n are sequences in 0 1 and r n 0 satisfying the conditions lim n n 0 n 1 n lim sup n n 1 lim inf n r n 0

generalized set valued variational inclusions in q uniformly smooth banach spaces abstract in this paper a class of generalized set valued variational inclusions in banach spaces are introduced and studied which include many variational inclusions studied by others in recent years by using some new and innovative techniques several existence theorems for the generalized set valued variational inclusions in q uniformly smooth banach spaces are established and some perturbed iterative algorithms for solving this kind of set valued variational inclusions are suggested and analyzed our results improve and generalize many known algorithms and results

the mann and ishikawa iterative approximation of solutions to variational inclusions with accretive type mappings abstract the purpose of this paper is to introduce and study the existence of solutions and convergence of mann and ishikawa iterative processes for a class of variational inclusions with accretive type mappings in banach spaces the results presented in this paper extend and improve the corresponding results of 1 9

strong convergence of iteration algorithms for a countable family of nonexpansive mappings abstract for a countable family t n n 1 of nonexpansive mappings a strong convergence of halpern type iteration is shown in order to find a common fixed point of t n n 1 in a reflexive banach space when n 0 1 satisfies the conditions c1 lim n n 0 and c2 n 1 n and several examples satisfying the condition b is given also we also research the strong convergence of the proximal point algorithm finally we apply our results to solve the equilibrium problems and variational inequalities for continuous monotone mappings

convergence theorems for multivalued φ hemicontractive operators and φ strongly accretive operators abstract suppose e is a uniformly smooth banach space and t e 2e is a multivalued hemicontractive operator with bounded range suppose an bn cn and an bn cn are real sequences in 0 1 satisfying the following conditions i a n b n c n a n b n c n 1 for all n n ii lim n b n lim n b n lim n c n 0 iii n 1 b n iv c n o b n for arbitrary xi u1 v1 e define the sequence xn n 1 by xn 1 anxn bn n cnun n tyn n n yn a nxn b n n c nvn n txn n n where un n 1 vn n 1 are arbitrary bounded sequences in e then xn n 1 converges strongly to the unique fixed point of t related results deal with the iterative solutions of nonlinear multivalued accretive operator equation f tx

stability of iterative procedures with errors for approximating common fixed points of a couple of q contractive like mappings in banach spaces abstract recently agarwal cho li and huang r p agarwal y j cho j li n j huang stability of iterative procedures with errors approximating common fixed points for a couple of quasi contractive mappings in q uniformly smooth banach spaces j math anal appl 272 2002 435 447 introduced the new iterative procedures with errors for approximating the common fixed point of a couple of quasi contractive mappings and showed the stability of these iterative procedures with errors in banach spaces in this paper we introduce a new concept of a couple of q contractive like mappings q 1 in a banach space and apply these iterative procedures with errors for approximating the common fixed point of the couple of q contractive like mappings the results established in this paper improve extend and unify the corresponding ones of agarwal cho li and huang r p agarwal y j cho j li n j huang stability of iterative procedures with errors approximating common fixed points for a couple of quasi contractive mappings in q uniformly smooth banach spaces j math anal appl 272 2002 435 447 chidume c e chidume approximation of fixed points of quasi contractive mappings in l p spaces indian j pure appl math 22 1991 273 386 chidume and osilike c e chidume m o osilike fixed points iterations for quasi contractive maps in uniformly smooth banach spaces bull korean math soc 30 1993 201 212 liu q h liu on naimpally and singh s open questions j math anal appl 124 1987 157 164 q h liu a convergence theorem of the sequence of ishikawa iterates for quasi contractive mappings j math anal appl 146 1990 301 305 osilike m o osilike a stable iteration procedure for quasi contractive maps indian j pure appl math 27 1996 25 34 m o osilike stability of the ishikawa iteration method for quasi contractive maps indian j pure appl math 28 1997 1251 1265 and many others in the literature

on the regularity condition in a convex feasibility problem abstract the regularity properties of a family of closed convex sets with nonempty intersection are investigated in the frame of a real hilbert space the significant role of these properties in solving convex feasibility problems with projection algorithms is pointed out

graph convergence for the h accretive operator in banach spaces with an application abstract in this paper a concept of graph convergence concerned with the h accretive operator is introduced in banach spaces and some equivalence theorems between of graph convergence and resolvent operator convergence for the h accretive operator sequence are proved as an application a perturbed algorithm for solving a class of variational inclusions involving the h accretive operator is constructed under some suitable conditions the existence of the solution for the variational inclusions and the convergence of iterative sequence generated by the perturbed algorithm are also given

experimental validation of performance limits and design guidelines for small antennas the theoretical limit for small antenna performance that was derived decades ago by wheeler and chu governs design tradeoffs for size bandwidth and efficiency theoretical guidelines have also been derived for other details of small antenna design such as permittivity aspect ratio and even the nature of the internal structure of the antenna in this paper we extract and analyze experimental performance data from a large body of published designs to establish several facts that have not previously been demonstrated 1 the theoretical performance limit for size bandwidth and efficiency are validated by all available experimental evidence 2 although derived for electrically small antennas the same theoretical limit is also generally a good design rule for antennas that are not electrically small 3 the theoretical predictions for the performance due to design factors such as permittivity aspect ratio and the internal structure of the antenna are also supported by the experimental evidence the designs that have the highest performance are those that involve the lowest permittivity have an aspect ratio close to unity and for which the fields fill the minimum size enclosing sphere with the greatest uniformity this work thus validates the established theoretical design guidelines

strong law of large numbers for the l1 karcher mean abstract sturm s strong law of large numbers in cat 0 spaces has been an influential tool to study the geometric mean or also called karcher barycenter of positive definite matrices it provides an easily computable stochastic approximation based on inductive means convergence of a deterministic version of this approximation has been proved by holbrook providing his nodice theorem for the karcher mean of positive definite matrices the karcher mean has also been extended to the infinite dimensional case of positive operators on a hilbert space by lawson lim and then to probability measures with bounded support by the second author however the cat 0 property of the space is lost and one defines the mean as the unique solution of a nonlinear operator equation on a convex banach finsler manifold the formulations of sturm s strong law of large numbers and holbrook s nodice approximation are natural and both conjectured to converge however all previous techniques of their proofs break down due to the banach finsler nature of the space in this paper we prove both conjectures by establishing the most general l 1 form of sturm s strong law of large numbers and holbrook s nodice theorem in the operator norm by developing a stochastic discrete time resolvent flow for the karcher barycenter using its wasserstein contraction property

weak and strong convergence theorems for fixed points of pseudocontractions and solutions of monotone type operator equations abstract let h be a real hilbert space k a nonempty closed convex subset of h and t k k a lipschitz pseudocontraction with a nonempty fixed point set weak and strong convergence theorems for the iterative approximation of fixed points of t are proved furthermore if t h h is a lipschitz monotone operator and f r t where r t denotes the range of t weak and strong convergence theorems for the iterative approximation of solutions of the operator equation tx f are proved

the equivalence between the convergence of ishikawa and mann iterations with errors for strongly successively pseudocontractive mappings without lipschitzian assumption abstract in this paper we prove some new equivalences between convergence of the ishikawa and mann iteration sequences with errors in two schemes by xu y g xu ishikawa and mann iteration process with errors for nonlinear strongly accretive operator equations j math anal appl 224 1998 91 101 and liu l s liu ishikawa and mann iterative process with errors for nonlinear strongly accretive mappings in banach spaces j math anal appl 194 1995 114 125 respectively for strongly successively pseudocontractive mappings our main results improve and extend the corresponding results of the all references listed in this article

approximation solvability of nonlinear random a η resolvent operator equations with random relaxed cocoercive operators in this paper we introduce and study a new class of nonlinear random a h resolvent operator equations with random relaxed cocoercive operators in hilbert spaces by using chang s lemma theorem 3 1 of liu and li and the resolvent operator technique for a h monotone operators due to lan we also prove the existence theorems of the solutions and convergence theorems of the new generalized random iterative procedures with errors for this nonlinear random a h resolvent operator equations involving non monotone random set valued operators in hilbert spaces the results presented in this paper improve and generalize some known corresponding results in the literature

general a monotone operators and perturbed iterations for nonlinear set valued relaxed cocoercive operator inclusion problems in this paper we introduce the notion of general a monotone operators in banach spaces study some properties of general a monotone operator and the new proximal mapping associated with the general a monotone operators by using alber s inequalities nalder s results and the new proximal mapping technique we also construct two new class of perturbed iterative algorithms with mixed errors for solving a new class of nonlinear set valued relaxed cocoercive operator inclusions and study applications of general a monotone operators to the approximation solvability of the nonlinear set valued relaxed cocoercive operator inclusion problems in banach spaces furthermore the general a monotone operators are illustrated by some examples the results presented in this paper improve and generalize the corresponding results on strongly monotone quasi variational inclusions and nonlinear implicit quasi variational inclusions

stable iteration procedures for strong pseudocontractions and nonlinear equations involving accretive operators without lipschitz assumption abstract let e be a real uniformly smooth banach space and t e e a strong pseudocontraction with a bounded range we prove that the mann and ishikawa iteration procedures are t stable some related results deal with the stability of these procedures for the iteration approximation of solutions of nonlinear equations involving accretive operators our results improve and or extend those corresponding results announced by osilike

convergence theorems for strict pseudo contractions in q uniformly smooth banach spaces abstract in this paper we discuss some properties of iterates generated by a strict pseudo contraction or a finite family of strict pseudo contractions in a real q uniformly smooth banach space we prove the weak convergence and strong convergence of pseudo contractive mappings the results presented in this paper are interesting extensions and improvements upon those known ones of marino and xu g marino h k xu weak and strong convergence theorems for strict pseudo contractions in hilbert spaces j math anal appl 329 2007 336 349 acedo and xu g l acedo h k xu iterative methods for strict pseudo contractions in hilbert spaces nonlinear anal 67 2007 2258 2271 and zhou h zhou convergence theorems for strict pseudo contractions in 2 uniformly smooth banach spaces nonlinear anal 69 2008 3160 3173

modified noor iterations for nonlinear equations in banach spaces the purpose of this paper is to analyze the modified three step iterative scheme for solving nonlinear operator equations in real banach spaces our results can be viewed as an extension of three step and two step iterative schemes of glowinski and le tallec r glowinski p le tallec augemented lagrangian and operator splitting methods in nonlinear mechanics siam publishing co philadelphia 1989 noor m a noor three step iterative algorithms for multivalued quasi variational inclusions j math anal appl 255 2001 589 604 m a noor some predictor corrector algorithms for multivalued variational inequalities j optim theory appl 108 3 2001 659 670 m a noor t m rassias z huang three step iterations for nonlinear accretive operator equations j math anal appl 274 2002 59 68 and ishikawa s ishikawa fixed points by a new iteration method proc amer math soc 44 1974 147 150

global existence and mann iterative algorithms of positive solutions for first order nonlinear neutral delay differential equations abstract this paper deals with the first order nonlinear neutral delay differential equation d dt x t p t x t f t x 1 t x 2 t x n t 0 t t 0 where 0 p c t 0 r f c t 0 r n r and l c t 0 r with limt l t for l 1 2 n by using the banach fixed point theorem we prove the global existence of uncountably many bounded positive solutions for the above equation relative to all ranges of the function p construct some mann type iterative algorithms with errors to approximate these positive solutions and discuss several error estimates between the sequences generated by the iterative algorithms and these positive solutions seven examples are presented to illuminate the results obtained in this paper

strong convergence of viscosity approximation methods for finding zeros of accretive operators in banach spaces abstract in this paper we introduce a composite iterative scheme by viscosity approximation method for finding a zero of an accretive operator in banach spaces then we establish strong convergence theorems for the composite iterative scheme the main theorems improve and generalize the recent corresponding results of kim and xu t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 2005 51 60 qin and su x qin y su approximation of a zero point of accretive operator in banach spaces j math anal appl 329 2007 415 424 and xu h k xu strong convergence of an iterative method for nonexpansive and accretive operators j math anal appl 314 2006 631 643 as well as aoyama et al k aoyama y kimura w takahashi m toyoda approximation of common fixed points of a countable family of nonexpansive mappings in banach spaces nonlinear anal 67 2007 2350 2360 benavides et al t d benavides g l acedo h k xu iterative solutions for zeros of accretive operators math nachr 248 249 2003 62 71 chen and zhu r chen z zhu viscosity approximation fixed points for nonexpansive and m accretive operators fixed point theory and appl 2006 2006 1 10 and kamimura and takahashi s kamimura w takahashi approximation solutions of maximal monotone operators in hilberts spaces j approx theory 106 2000 226 240

generalized set valued variational inclusions and resolvent equations in banach spaces abstract in this paper we construct a new iterative algorithm for set valued variational inclusions without the compactness condition and study the convergence of the perturbed ishikawa iterative process for solving a class of the generalized single valued variational inclusions in banach spaces the result obtained in this paper is a generalization and improvement of noor s theorem 1

convergence theorems for fixed points of uniformly continuous generalized φ hemi contractive mappings abstract let e be a real normed linear space k be a nonempty subset of e and t k e be a uniformly continuous generalized hemi contractive mapping i e f t x k t x x and there exist x f t and a strictly increasing function 0 0 0 0 such that for all x k there exists j x x j x x such that t x x j x x x x 2 x x a if y k is a fixed point of t then y x and so t has at most one fixed point in k b suppose there exists x 0 k such that the sequence x n defined by x n 1 a n x n b n t x n c n u n n 0 is contained in k where a n b n and c n are real sequences satisfying the following conditions i a n b n c n 1 ii n 0 b n c n iii n 0 b n c n 2 iv n 0 c n and u n is a bounded sequence in e then x n converges strongly to x in particular if y is a fixed point of t in k then x n converges strongly to y a related result deals with the iterative approximation of the zeros of uniformly continuous generalized quasi accretive mappings

a general iterative scheme for k strictly pseudo contractive mappings and optimization problems in this paper we introduce a new general iterative scheme for finding fixed points of a strictly pseudo contractive mapping and then prove that the sequence generated by the proposed iterative scheme converges strongly to a fixed point of the mapping which is a solution of a certain optimization problem related to a strongly positive bounded linear operator additional results of the main result are also obtained