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

on a higher order secant method in this paper we carry out a modification of the classical secant method our goal is to accelerate the convergence until order two but without using any derivative two convergence theorems are presented finally some numerical experiments are analyzed

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

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

nonlinear analysis of cross ply thick cylindrical shells under axial compression abstract buckling postbuckling nonlinear vibration and parametric resonance of thick circular cylindrical shells under axial compression are analyzed in this paper the theory developed is based on a nonlinear and non shallow thick shell theory with its final equations involving two unknowns the circumferential displacement v and the radial displacement w the shell wall is cross ply laminated the plies are specially orthotropic but the lamination can be unsymmetric the axial load is assumed to be harmonically time dependent or constant as a special case the governing nonlinear partial differential equations are reduced to nonlinear ordinary differential equations in terms of time by the galerkin procedure then an asymptotic method is used to solve the resulting nonlinear ordinary differential equations the numerical results for buckling loads are shown to compare very well with those of three dimensional theories in the literature even for very thick shells the effects of lay up and thickness on postbuckling equilibrium nonlinear vibration and parametric resonance are demonstrated by examples

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

improving the applicability of the secant method to solve nonlinear systems of equations a modification of the secant method for the approximation of nonlinear system of equations is considered to improve the applicability of the secant method this modification changes the resolution of a linear system in each step necessary to apply the secant method for several matrix multiplications in this way the numerical stability of the secant method can be improved in addition in this paper we prove that the modification considered keeps two important properties of the secant method such as does not use derivatives in its algorithm and has r order of convergence at least 1 5 2

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

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

plastic buckling of circular cylindrical shells under combined in plane loads abstract a study of plastic buckling of a circular cylindrical shell subject to axial torsional and circumferential loading stresses is presented in the deformation model the transverse shear is taken into account by a first order theory with a correction factor for the buckled equilibrium the contributions of both v circumferential displacement and w normal displacement to the buckling are included so that a better accuracy can be achieved j2 deformation theory and j2 flow theory of plasticity are used for the establishment of the constitutive relations for buckling analysis with the existence of torsional load the equation of radial equilibrium includes the term of mixed second order derivative 2 w x y and the plastic in plane stress strain relations are anisotropic and therefore a handy form of solution in terms of trigonometric functions is no longer possible consequently the finite difference method is used to improve the accuracy a five point finite difference scheme is employed instead of the conventional central difference numerical results of examples show the interactive roles of the in plane loads in the plastic buckling

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

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

an error analysis for the secant method sharp a priori and a posteriori error bounds are given for the secant method for solving non linear equations in banach spaces the numerical stability of this method is also investigated the stability results are analogous to those obtained by lancaster for newton s method

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

on the existence and iterative approximation problems of solutions for set valued variational inclusions in banach spaces the purpose of this paper is to introduce and study a class of set valued variational inclusions in banach spaces by using michael s selection theorem and nadler s theorem some existence theorems and iterative algorithms for solving this kind of set valued variational inclusion in banach spaces are established and suggested

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

extending the convergence domain of the secant and moser method in banach space we present a new semilocal convergence analysis for the secant and the moser method in order to approximate a solution of an equation in a banach space setting using the method of recurrent relations and weaker sufficient convergence criteria than in earlier studies such as amat et al 2014 hernandez and rubio 2007 hernandez and rubio 1999 and hernandez and rubio 2002 we increase the convergence domain of these methods the advantages are also obtained under less computational cost than in amat et al 2014 hernandez and rubio 2007 hernandez and rubio 1999 and hernandez and rubio 2002 numerical examples where the older convergence criteria are not satisfied but the new convergence criteria are satisfied are also provided in this study

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

non linear vibration and postbuckling of unsymmetric cross ply circular cylindrical shells abstract based on von karman donnell kinematic assumptions for laminated shells the non linear vibration and postbuckling behaviour of unsymmetrically laminated cross ply circular cylindrical shells with clamped and simply supported ends are studied by a multi mode approach a solution is formulated and satisfies the associated compatibility equation and all boundary conditions the transverse equation of motion is fulfilled by the galerkin procedure in the case of non linear vibration problems the solution is obtained by the method of harmonic balance the effect of initial imperfection is also included results in non linear vibration and postbuckling are presented for different amplitudes of initial imperfection and four sets of boundary conditions present results are compared with available data

approximation methods for nonlinear operator equations of the m accretive type abstract let e be a real banach space which is both uniformly convex and uniformly smooth let t d t e e be m accretive where the domain of t d t is a proper subset of e for any e approximation methods are constructed which converge strongly to a solution of the operator equation x tx explicit error estimates are obtained a related result deals with operator equations of the dissipative type

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

nonlinear theory for plates and shells including the effects of transverse shearing nonlinear strain displacement relations for three dimensional elasticity are determined in orthogonal curvilinear coordinates to develop a two dimensiona l theory the displacements are expressed by trigonometric series representation through the thickness the nonlinear strain displacement relations are expanded into a series that contains all first and second degree terms in the series for the displacements only the first few terms are retained insertion of the expansions into the three dimensional virtual work expression leads to nonlinear equations of equilibrium for laminated and thick plates and shells that include the effects of transverse shearing equations of equilibrium and buckling equations are derived for flat plates and cylindrical shells the shell equations reduce to conventional transverse shearing shell equations when the effects of the trigonometric terms are omitted and to classical shell equations when the trigonometric terms are omitted and the shell is assumed to be thin numerical results are presented for the buckling of a thick simply supported flat rectangular plate in longitudinal compression

characteristic inequalities of uniformly convex and uniformly smooth banach spaces abstract let x be a real banach space with dual x and moduli of convexity and smoothness x e and x respectively for 1 p denotes the duality mapping from x into 2 x with gauge function t p 1 and j p denotes an arbitrary selection for j p let a r 0 0 t is strictly increasing and there exists c 0 such that t c x t 2 and f r 0 0 t is convex nondecreasing and there exists k 0 such that k x it is proved that x is uniformly convex if and only if there is a a such that x y p x p p j p x y x y x y x and x is uniformly smooth if and only if there is a f such that x y p x p p j p x y x y x y x where for given function f f x y is defined by f x y p 0 1 x ty x p t f t y x ty x dt these inequalities which have various applications can be regarded as general banach space versions of the well known polarization identity occurring in hilbert spaces

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

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

iterative approximation of solutions to nonlinear equations involving m accretive operators in banach spaces let e be an arbitrary real banach space and t e e be a lipschitz continuous accretive operator under the lack of the assumption limn n limn n 0 we prove that the ishikawa iterative sequence with errors converges strongly to the unique solution of the equation x tx f moreover this result provides a convergence rate estimate for some special cases of such a sequence utilizing this result we imply that if t e e is a lipschitz continuous strongly accretive operator then the ishikawa iterative sequence with errors converges strongly to the unique solution of the equation tx f our results improve generalize and unify the ones of liu chidume and osilike and to some extent of reich

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

expanding the applicability of the secant method under weaker conditions abstract we present a new semilocal convergence analysis for secant method in order to approximate a locally unique solution of a nonlinear equation in a banach space setting our analysis includes the computation of the bounds on the limit points of the majorizing sequences involved under the same computational cost on the parameters involved our convergence criteria are weaker and the error bounds more precise than in earlier studies such as amat and busquier 2003 amat et al in press argyros and hilout 2012 argyros et al 2014 argyros and magrenan 2014 2015 dennis 1971 ezquerro et al 2000 ortega and rheinboldt 1970 potra and ptak 1984 schmidt 1978 numerical examples are also presented to illustrate the theoretical results obtained in this study

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 iterative solution of the equation f x tx for a monotone operator t in lp spaces suppose t is a multivalued monotone operator not necessarily continuous with open domain d t in lp 2 p f r i t and the equation f x tx has a solution q d t then there exists a neighbourhood b d t of q and a real number r1 0 such that for any r r1 for any initial guess x1 b and any singlevalued section t0 of t the sequence xn n 1 generated from x1 by xn 1 1 cn xn cn f t0xn remains in d t and converges strongly to q with xn q 0 n 1 2 furthermore for x lp e e

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

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

inequalities in banach spaces with applications well known that many problems in a hilbert space h are solved by applying the following identity ilax 1 a yi12 a412 1 llyl12 a 1 mx yl12 1 1 for all x y in h and 0 5 i 5 1 therefore one natural method to solve problems in a banach space xis to establish equalities and usually inequalities in xanalogous to 1 1 this is in fact shown by some authors recent work see for example reich l poffald and reich 2 lim 3 lim et af 4 prus and smarzewski 5 smarzewski 6 and reich 21 the purpose of this paper is to continue carrying out investigations in this line more precisely in section 3 we establish some inequalities analogous to 1 l in either uniformly convex or uniformly smooth banach spaces as corollaries we obtain new characteristics of p uniform convexity and q uniform smoothness of a banach space x via the functionals i lip and ii llq respectively we give in section 4 applications of the inequalities obtained in section 3 to fixed points of uniformly lipschitzian mappings and to best approximation theory

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

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