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

convergence theorems for strongly pseudo contractive and strongly accretive maps supposeeis an arbitrary real banach space andkis a nonempty closed convex and bounded subset ofe supposet k kis a uniformly continuous strong pseudo contraction with constantk 0 1 suppose an bn cn a n b n and c n are sequences in 0 1 satisfying the following conditions i an bn cn 1 a n b n c n integersn 0 ii lim bn lim b n lim c n 0 iii bn iv cn for arbitraryx0 u0 v0 k define the sequence xn n 0iteratively byxn 1 anxn bntyn cnun yn a nxn b ntxn c nvn n 0 where un vn are arbitrary sequences ink then xn converges strongly to the unique fixed point oft related results deal with the iterative solutions of nonlinear equations involving set valued strongly accretive operators

new iteration procedures with errors for multivalued φ strongly pseudocontractive and φ strongly accretive mappings abstract the purpose of this paper is to introduce and study a new class of ishikawa iteration processes with errors for multivalued mappings in real banach spaces some convergence theorems of ishikawa iteration sequences with errors for approximation of the fixed points of multivalued strongly pseudocontractive mappings and approximation of the solutions of nonlinear equations with strongly accretive mappings are obtained respectively our results improve and extend some recent results in this field

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

distributed 3 d localization of camera sensor networks from 2 d image measurements in this paper we propose distributed algorithms that use 2 d image measurements to estimate the absolute 3 d poses of the nodes in a camera network with the purpose of enabling higher level tasks such as tracking and recognition we assume that pairs of cameras with overlapping fields of view can estimate their relative 3 d pose rotation and translation direction using standard computer vision techniques the solution we propose combines these local noisy estimates into a single consistent localization we derive our algorithms from optimization problems on the manifold of poses we provide theoretical results on the convergence of the algorithms choice of the step size initialization and on the properties of their solutions sensitivity uniqueness we also provide experiments on synthetic and real data interestingly our algorithm for estimating the rotation part of the poses shows some degree of robustness to outliers

geodesic regression and the theory of least squares on riemannian manifolds this paper develops the theory of geodesic regression and least squares estimation on riemannian manifolds geodesic regression is a method for finding the relationship between a real valued independent variable and a manifold valued dependent random variable where this relationship is modeled as a geodesic curve on the manifold least squares estimation is formulated intrinsically as a minimization of the sum of squared geodesic distances of the data to the estimated model geodesic regression is a direct generalization of linear regression to the manifold setting and it provides a simple parameterization of the estimated relationship as an initial point and velocity analogous to the intercept and slope a nonparametric permutation test for determining the significance of the trend is also given for the case of symmetric spaces two main theoretical results are established first conditions for existence and uniqueness of the least squares problem are provided second a maximum likelihood criteria is developed for a suitable definition of gaussian errors on the manifold while the method can be generally applied to data on any manifold specific examples are given for a set of synthetically generated rotation data and an application to analyzing shape changes in the corpus callosum due to age

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

iterative solutions of nonlinear accretive operator equations in arbitrary banach spaces suppose e is an arbitrary real banach space and k is a nonempty closed convex and bounded subset of e suppose t k k is a uniformly continuous strong pseudocontraction it is proved that the mann and the ishikawa iteration methods converge strongly to the unique fixed point of t furthermore our results also hold for the slightly more general class of strictly hemicontractive maps related results deal with the iterative approximation of solutions of accretive operator equations in arbitrary real banach spaces miramare trieste april 1996 permanent address department of mathematics university of nigeria nsukka nigeria

some problems and results in the study of nonlinear analysis this paper is presented as a survey of the latest and new results on some topics in the study of nonlinear analysis which were obtained by the author and some chinese mathematicians

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

a generalized steepest descent approximation for the zeros of m accretive operators a necessary and sufficient condition is proved for a generalized steepest descent approximation to converge to the zeros of m accretive operators related results deal with the convergence of the scheme to fixed points of pseudocontractive maps

on the equivalence of the convergence criteria between modified mann ishikawa and multi step iterations with errors for successively strongly pseudo contractive operators abstract in this paper the equivalence of the convergence between the modified mann ishikawa and multi step noor iterations with errors is proven for the successively strongly pseudo contractive operators without lipschitzian assumption our results generalize the recent results of the paper b e rhoades s m soltuz the equivalence between mann ishikawa iterations and multi step iteration nonlinear anal 58 2004 219 228 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 pseudo contractive maps j math anal appl 289 2004 266 278 by extending to the more generalized multi step iterations with errors and hence improve the corresponding results of all the references in bibliography by providing the equivalences of convergence between all of these up to date iteration schemes

error scaling laws for linear optimal estimation from relative measurements in this paper we study the problem of estimating vector valued variables from noisy ldquorelativerdquo measurements which arises in sensor network applications the problem can be posed in terms of a graph whose nodes correspond to variables and edges to noisy measurements of the difference between two variables the optimal minimum variance linear unbiased estimate of the node variables with an arbitrary variable as the reference is considered this paper investigates how the variance of the estimation error of a node variable grows with the distance of the node to the reference node a classification of graphs namely dense or sparse in rd 1 les d les 3 is established that determines this growth rate in particular if a graph is dense in 1 d 2 d or 3 d a node variable s estimation error is upper bounded by a linear logarithmic or bounded function of distance from the reference corresponding lower bounds are obtained if the graph is sparse in 1 d 2 d and 3 d these results show that naive measures of graph density such as node degree are inadequate predictors of the estimation error being true for the optimal linear unbiased estimate these scaling laws determine algorithm independent limits on the estimation accuracy achievable in large graphs

perturbed iterative process for fixed points of multivalued φ hemicontractive mappings in banach spaces abstract in this paper the unique fixed point of multivalued hemicontractive mapping is approximated by a perturbed iteration method in arbitrary real banach spaces

needle crystal formation in two dimensions a simple model based on conformal mapping is constructed to simulate the two dimensional growth of needle crystals growing out regularly from a common point the resulting patterns are very similar to those which were obtained by other methods the radius of gyration exponent beta is measured and found to be in the range 0 58 0 65 independent of the number of needles n it is shown that for large patterns beta asymptotically approaches a value of 2 3 to compare the patterns with the dla aggregates the average slope alpha was measured for the density density correlation function plotted logarithmically log r to log c r the relation between alpha and beta which is characteristic of dla fractal aggregates is satisfied only in the case n 8

error bounds for approximation solutions to nonlinear equations of strongly accretive operators in uniformly smooth banach spaces abstract let x be a uniformly smooth banach space and t x x a strongly accretive operator in this paper we give the error bounds for the approximation solutions of the nonlinear equation tx f generated by both the mann and the ishikawa iteration process on the other hand let k be a nonempty convex subset of x and t k k a strictly pseudocontractive mapping the related results deal with the error bounds for the iterative approximation of the fixed point of t generated by these two processes

iterative process with errors to nonlinear ф strongly accretive operator equations in arbitrary banach spaces abstract let x be an arbitrary banach space and t d t x x be a lipschitz strongly accretive operator with domain d t and range r t the mann and ishikawa type iterative sequences with errors which strongly converge to the unique solution of the equation tx f under weaker conditions are given the related results deal with the problems that the mann and ishikawa iterative sequences with errors strongly converge to the unique fixed point of lipschitz hemicontractive operators

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

sensor network localization on the group of three dimensional displacements we consider the problem of estimating relative configurations of nodes in a sensor network based on noisy measurements by exploiting the cyclic constraints induced by the sensing topology to the network we derive a constrained optimization on se 3 n for the case of a network with a single cyclic constraint we present a closed form solution we show that in certain cases namely restriction to pure rotation and pure translation this solution is independent of the particular representation of the constraint function and is the unique constrained minimizer of an appropriate cost for sensing topologies represented by a general weakly connected digraph we present a solution method which is based on the limits of the solution curves of a continuous time ordinary differential equation we show that solutions obtained by our method satisfy all semicycle generalized cycle constraints induced by the sensing topology of the network further we show through numerical simulation that for gaussian like

iterative solutions of nonlinear equations with φ strongly accretive operators in uniformly smooth banach spaces abstract suppose that x is a uniformly smooth banach space and t x x is a demicontinuous not necessarily lipschitz strongly accretive operator it is proved that the ishikawa iterative method with errors converges strongly to the solutions of the equations f tx and f x tx respectively a related result deals with the approximation of fixed points of strongly pseudocontractive operators our results extend improve and unify the recent results obtained by chidume 1 2 and zhou 3

iterative solution of nonlinear equations with strongly accretive operators abstract let e be a real banach space with a uniformly convex dual suppose t e e is a strongly accretive map with bounded range such that for each e the equation tx has a solution in e it is proved that each of the two well known fixed point iteration methods the mann and ishikawa iteration methods under suitable conditions converges strongly to a solution of the equation tx furthermore our method shows that such a solution is necessarily unique explicit error estimates are given our results resolve in the affirmative an open problem j math anal appl 151 no 2 1990 460 and generalize important known results

the solution by iteration of nonlinear equations of hammerstein type let e be a real uniformly smooth banach space suppose n is a set valued locally accretive map with open domain d n c e k is a single valued map with domain d k c e such that im n c d k and k exists and is locally strongly accretive on im k if the equation f e x knx has a solution x e d n the strong convergence of iteration methods of the ishikawa and mann types to this solution is established related theorems deal with the iterative solution of nonlinear equations of the form f g x tx for the case where t is accretive explicit convergence rates are established miramare trieste november 1996 permanent address department of mathematics and computer science nnamdi azikiwe university p m b 5025 awka anambra state nigeria

projection like retractions on matrix manifolds this paper deals with constructing retractions a key step when applying optimization algorithms on matrix manifolds for submanifolds of euclidean spaces we show that the operation consisting of taking a tangent step in the embedding euclidean space followed by a projection onto the submanifold is a retraction we also show that the operation remains a retraction if the projection is generalized to a projection like procedure that consists of coming back to the submanifold along admissible directions and we give a sufficient condition on the admissible directions for the generated retraction to be second order this theory offers a framework in which previously proposed retractions can be analyzed as well as a toolbox for constructing new ones illustrations are given for projection like procedures on some specific manifolds for which we have an explicit easy to compute expression

a characteristic condition for convergence of steepest descent approximation to accretive operator equations in the present paper a sufficient and necessary condition for convergence of steepest descent approximation to accretive operator equations is established and for the sufficiency part a specific error estimation is also given

a perturbed iterative procedure for multivalued pseudo contractive mappings and multivalued accretive mappings in banach spaces abstract the main purpose of this paper is to introduce and study a new perturbed iteration method for multivalued mappings some strong convergence theorems of perturbed iteration sequences for multivalued pseudo contractive mappings and strongly accretive mappings are obtained

accumulation and control of random errors in the ishikawa iterative process in arbitrary banach space the purpose of this note is to study directly the relation between random errors and two parameter sequences in the ishikawa iterative process and to estimate the accumulation of errors in the iterative process the obtained results show that when one of the sequences converges to zero the accumulation of errors is bounded if the other sequence is non summable while the accumulation of errors is controllable in a permissible range if the sequence is summable

stable iteration procedures for strong pseudo contractions and nonlinear operator equations of the accretive type it is proved that certain mann and ishikawa iteration procedures arestable with respect to strongly pseudo contractive mappingsin real banach spaces which areq uniformly smooth 1 q a related result deals with stable iteration procedures forsolutions of nonlinear equations of the accretive 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

fingered growth in channel geometry a loewner equation approach a simple model of laplacian growth is considered in which the growth takes place only at the tips of long thin fingers following carleson and makarov l carleson and n makarov j anal math 87 103 2002 the evolution of the fingers is studied with use of the deterministic loewner equation the method is then extended to study the growth in a linear channel with reflecting sidewalls one and two finger solutions are found and analyzed it turns out that the presence of the walls has a significant influence on the shapes of the fingers and the dynamics of the screening process in which longer fingers suppress the growth of the shorter ones

sensor network localization with imprecise distances an approach to formulate geometric relations among distances between nodes as equality constraints is introduced in this paper to study the localization problem with imprecise distance information in sensor networks these constraints can be further used to formulate optimization problems for distance estimation the optimization solutions correspond to a set of distances that are consistent with the fact that sensor nodes live in the same plane or 3d space as the anchor nodes these techniques serve as the foundation for most of the existing localization algorithms that depend on the sensors distances to anchors to compute each sensor s location 2006 elsevier b v all rights reserved

steepest descent method for equilibrium points of nonlinear systems with accretive operators let e be a real normed linear space and let a e 2e be a bounded uniformly continuous strongly accretive multi valued map with nonempty closed values such that the inclusion 0 ax has a solution x e it is proved that both the ishikawa and the mann iteration processes are bounded and converge strongly to x related results deal with the convergence of the iteration processes to fixed points of strongly pseudocontractive maps and the iterative solution of the equation 0 x fx for an accretive map f furthermore the ishikawa and mann iteration methods with errors are discussed and proofs are sketched on how our theorems extend to these methods our method of proof is of independent interest

iterative solution of nonlinear equations involving strongly accretive operators without the lipschitz assumption abstract letebe a real banach space with a uniformly convex dual spacee supposet e eis a continuous not necessarily lipschitzian strongly accretive map such that i t has bounded range whereidenotes the identity operator it is proved that the ishikawa iterative sequence converges strongly to the unique solution of equationtx f f e our results extend and complement the recent results obtained by chidume

stability of iterative procedures with errors approximating common fixed points for a couple of quasi contractive mappings in q uniformly smooth banach spaces in this paper we introduce the new iterative sequences with errors approximating the common fixed point for a couple of quasi contractive mappings and show the stability of the iterative procedures with errors in q uniformly smooth banach spaces our results extend improve and unify the corresponding results of chidume osilike liu and others

asymptotic number of needles in laplacian growth using linear stability analysis the authors argue that the asymptotic number of needles growing out of a center in a laplacian process is two in all dimensions special arrangements in two dimensions can be solved by conformal mapping

an iterative process for nonlinear lipschitzian strongly accretive mappings in lp spaces abstract suppose x l p or l p p 2 let t x x be a lipschitzian and strongly accretive map with constant k 0 1 and lipschitz constant l define s x x by sx f tx x let c n n 1 be a real sequence satisfying 1 i 0 c n k p 1 l 2 2 k 1 1 for each n 2 ii n c n then for arbitrary x 0 x the sequence x n 1 1 c n x n c n sx n n 0 converges strongly to the unique solution of tx f moreover if c n k p 1 l 2 2 k 1 1 for each n then x n 1 q n 2 x 1 q where q denotes the solution of tx f and 1 k p 1 l 2 2 k 1 1 0 1 a related result deals with the iterative approximation of lipschitz strongly pseudocontractive maps in x

convergence theorem for the common solution for a finite family of ϕ strongly accretive operator equations the purpose of this paper is to study a strong convergence of multi step iterative scheme to a common solution for a finite family of uniformly continuous strongly accretive operator equations in an arbitrary banach space as a consequence the strong convergence theorem for the multi step iterative sequence to a common fixed point for finite family of strongly pseudocontractive mappings is also obtained the results presented in this paper thus improve and extend the corresponding results of inchan 6 kang 8 9 and many others

on picard iterations for strongly accretive and strongly pseudo contractive lipschitz mappings abstract in this note we speed up the convergence of the picard sequence of iterations for strongly accretive and strongly pseudo contractive mappings our results improve the results of chidume c e chidume picard iteration for strongly accretive and strongly pseudo contractive lipschitz maps ictp preprint no ic2000098 c e chidume iterative algorithms for non expansive mappings and some of their generalizations in nonlinear analysis and applications to v lakshmikantham on his 80th birthday vol 1 2 kluwer acad publ dordrecht 2003 pp 383 429 and liu l liu approximation of fixed points of a strictly pseudo contractive mapping proc amer math soc 125 2 1997 1363 1366 and some other known results the technique of the proof presented in this paper is different from the technique used by chidume

on chidume s open questions and approximate solutions of multivalued strongly accretive mapping equations in banach spaces abstract some new convergence theorems of the ishikawa iteration process for multi valued pseudo contractive mappings and multi valued accretive mappings are obtained which affirmatively answer the open questions put forth by 4

simulating hydrodynamics a pedestrian model a hele shaw cell contains two fluids seperated by an interface because the fluids are held in a narrow regions between two plates the cell can be described by a set of two dimensional hydrodynamic equations which determine the velocity fields in the fluids as well as the motion of the interface between them a discretized version of these equations can be implemented in terms of the motion of random walkers the walkers have the effect of carrying pieces of the fluid from one place to another they simulate a discrete version of the laplace equation and obey the appropriate boundary conditions for the fluid the walker hydrodynamic connection is explored in the limiting situation in which the viscosity of one of the fluids vanishes an algorithm is constructed and a few exemplary simulations are shown

monte carlo approach to dendritic growth the connection between diffusion limited aggregation and the equations of dendritic growth is critically examined a different type of monte carlo simulation is proposed and used to construct two dimensional dendrite like patterns the wavelength occurring for short times is in good agreement with the linear stability analysis the time dependence of the characteristic wavelengths is also determined

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

ishikawa and mann iteration methods with errors for nonlinear equations of the accretive type abstract let e be an arbitrary banach space and t e e a lipschitz strongly accretive operator it is proved that for a given f e the ishikawa and the mann iteration methods with errors introduced by 18 converge strongly to the solution of the equation tx f furthermore if e is a uniformly smooth banach space and t e e is demicontinuous and strongly accretive it is also proved that both the ishikawa and the mann iteration methods with errors converge strongly to the solution of the equation tx f related results deal with the iterative approximation of fixed points of strongly pseudocontractive operators and the solution of the equation x tx f f e when t e e is m accretive

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

steepest descent approximations for accretive operator equations a necessary and sufficient condition is established for the strong convergence of the steepest descent approximation to a solution of equations involving quasi accretive operators defined on a uniformly smooth banach space miramare trieste march 1993

on the generalized implicit quasivariational inequalities abstract in the present paper we introduce and study a new class of generalized nonlinear implicit quasivariational inequalities for set valued mappings and construct some new iterative algorithms we prove the existence of solutions for this class of generalized nonlinear implicit quasivariational inequalities for set valued mappings without compactness and the convergence of iterative sequences generated by the algorithms we also study a new perturbed iterative algorithm for solving a class of general strongly nonlinear quasivariational inequalities

the mann process for perturbed m accretive operators in banach spaces this work was carried out while this author was visiting the university ofalabama in huntsville underthe nancial support by the lg yonam foundation 1998 and he would like to thank professor claudio h morales for his hospitality in the department of mathematics 0362 546x 01 see front matter 2001 elsevier science ltd all rights reserved pii s0362 546x 00 00115 2

iterative solution of nonlinear equations of the φ strongly accretive type abstract letq 1 and letebe a realq uniformly smooth banach space lett e ebe a lipschitz strongly accretive operator and suppose the equationtx f f e has a solution it is proved that under suitable conditions on the real sequences n n 0 and n n 0 the iteration process formula converges strongly to the unique solution of the equationtx f a related result deals with the approximation of fixed points of hemicontractive operators a class of operators which is much more general than the important class of strongly pseudocontractive operators

the exact solution of nonlinear operator equation aubu cu f abstract this paper is intended to discuss the problems of solving system of linear operator equations and a kind of nonlinear operator equation a u b u c u f for system of linear operator equations we obtain a criterion about the existence of solutions if it has solutions we get the analytic representation of its minimum norm solution and the structure of its solution space for nonlinear operator equation a u b u c u f with the help of the discussion on how to solve the system of linear operator equations the exact solution is given besides we obtain the representation of all its solutions

characteristic conditions for convergence of generalized steepest descent approximation to multivalued accretive operator equations abstract in the present paper sufficient and necessary conditions for convergence of generalized steepest descent approximation to multivalued accretive operator equations are established for the sufficiency part and a specific error estimation is also given

iterative approximations of fixed points and solutions for strongly accretive and strongly pseudo contractive mappings in banach spaces abstract in this article we prove some new convergence theorems of the ishikawa and mann iteration sequences for strongly accretive and strongly pseudo contractive mappings by using the new inequality and the new approximation methods our main results improve and extend the corresponding results of j math anal appl 151 1990 453 461 proc amer math soc 120 1994 545 551 j math appl 192 1995 502 518 j math anal appl 174 1993 441 449 acta appl math 32 1993 183 196 nonlinear anal tma 24 1995 981 987 j math anal appl 178 1993 9 21 proc amer math soc 125 6 1997 1705 1709

iterative process with errors for fixed points of multivalued φ hemicontractive operators in uniformly smooth banach spaces abstract let e be a uniformly smooth banach space and t e 2e be a not necessarily continuous multivalued o hemicontractive mapping this paper proves that under suitable conditions the multivalued 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 f tx when t e 2e is multivalued o strongly accretive these results generalize the results of the author 1 ding 2 3 osilike 4 5 zhou 6 7 and chidume 8 9 into more general multivalued o hemicontractive operators without the continuous assumption on operators t