Let K be a nonempty compact convex subset of a uniformly convex Banach space, and   K K T   : a multivalued nonexpansive mapping. We prove that the sequences of Noor iterate converge to a fixed point of T. This generalizes former results proved by Banach convergence of Noor iterates for a multi-valued mapping with a fixed point. We also introduce both of the iterative processes in a new sen...

In this paper, we propose a new hybrid subgradient algorithm for finding common point in the set of solutions pseudomonotone equilibrium problem and fixed points relatively nonexpansive mapping real uniformly convex smooth Banach spaces. Weak strong convergence iterative scheme are established. Our results generalizes improves several recent literature.

An iterative method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space has been studied. We prove a strong convergence theorem under mild assumptions.

We present a subgradient extragradient method for solving variational inequalities in Hilbert space. In addition, we propose a modified version of our algorithm that finds a solution of a variational inequality which is also a fixed point of a given nonexpansive mapping. We establish weak convergence theorems for both algorithms.

We discuss the following viscosity approximations with the weak contraction A for a nonexpansive mapping sequence {Tn}, yn αnAyn 1 − αn Tnyn, xn 1 αnAxn 1 − αn Tnxn. We prove that Browder’s and Halpern’s type convergence theorems imply Moudafi’s viscosity approximations with the weak contraction, and give the estimate of convergence rate between Halpern’s type iteration and Mouda’s viscosity ap...

We consider a mapping S of the form S =α0I+α1T1+α2T2+···+αkTk, where αi ≥ 0, α0 > 0, α1 > 0 and ∑k i=0αi = 1. We show that the Picard iterates of S converge to a common fixed point of Ti (i = 1,2, . . . ,k) in a Banach space when Ti (i = 1,2, . . . ,k) are nonexpansive.

In this paper, we introduce a general iterative scheme for finding a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of solutions of variational inequalities for an inverse-strongly monotone mapping.

Let $X$ be a reflexive Banach space, $T:Xto X$ be a nonexpansive mapping with $C=Fix(T)neqemptyset$ and $F:Xto X$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. In this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences ...

In this work, we suggest a general viscosity implicit midpoint rule for nonexpansive mapping in the framework of Hilbert space. Further, under certain conditions imposed on sequence parameters, strong convergence theorem is proved by generated proposed iterative scheme, which, addition, unique solution variational inequality problem. Furthermore, provide some applications to inequalities, Fredh...