The aim of paper is to prove a weak convergenceresult for finding a common of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for a monotone, Lipschitz continuous mapping. Using an example in C++, validity of the result will be proved. Also, we shall find a common element of the set of fixed points of a nonexpansive mapping and the ...

In this paper, we first prove a path convergence theorem for a nonexpansive mapping in a reflexive and strictly convex Banach space which has a uniformly Gâteaux differentiable norm and admits the duality mapping jφ, where φ is a gauge function on [0,∞). Using this result, strong convergence theorems for common fixed points of a countable family of nonexpansive mappings are established.

In this paper, we consider the convergence of three-step fixed point iterative processes for multivalued nonexpansive mapping, under some different conditions, the sequences of three-step fixed point iterates strongly or weakly converge to a fixed point of the multivalued nonexpansive mapping. Our results extend and improve some recent results. Mathematics Subject Classification: 47H09, 47H10, ...

An explicit hierarchical fixed point algorithm is introduced to solve the monotone variational inequality over the fixed point set of a nonexpansive mapping. This paper discusses a monotone variational inequality with variational constraint and convex optimization problems over the fixed point set of a nonexpansive mapping. The strong convergence for the proposed algorithm to the solution is gu...

We study the asymptotic behavior of the sequence of the iterates for a nonexpansive mapping, defined on a suitable subset of a Banach space with Opial's condition. Some results are stated also for semigroups of nonexpansive mappings and for mappings of asymptotically nonexpansive type in uniformly convex Banach spaces with Opial's condition.

The aim of this paper is to prove a common fixed point theorem for nonexpansive type single valued mappings which include both continuous and discontinuous mappings by relaxing the condition of continuity by weak reciprocally continuous mapping. Our result is generalize and extends the corresponding result of Jhade et al. [P.K. Jhade, A.S. Saluja and R. Kushwah, Coincidence and fixed points of ...

and Applied Analysis 3 R1 F T / ∅; R2 φ p, Tx ≤ φ p, x , for all x ∈ C, p ∈ F T ; R3 F T F̂ T . Definition 1.4. A point p ∈ C is said to be an strong asymptotic fixed point of T if C contains a sequence {xn}n 0 which converges strongly to p and limn→∞‖xn − Txn‖ 0. The set of strong asymptotic fixed points of T is denoted by F̃ T . We say that a mapping T is weak relatively nonexpansive see, e.g.,...

The purpose of this paper is to prove strong convergence theorems for common fixed points of two families of weak relatively nonexpansive mappings and a family of equilibrium problems by a new monotone hybrid method in Banach spaces. Because the hybrid method presented in this paper is monotone, so that the method of the proof is different from the original one. We shall give an example which i...

The aim of this paper is to prove strong and △-convergence theorems of modified S-iterative scheme for asymptotically quasi-nonexpansive mapping in hyperbolic spaces. The results obtained generalize several results of uniformly convex Banach spaces and CAT(0) spaces. KeywordsHyperbolic space, fixed point, asymptotically quasi nonexpansive mapping, strong convergence, △-convergence.

We prove the weak and strong convergence of the implicit iterative process to a common fixed point of an asymptotically quasi-I-nonexpansive mapping T and an asymptotically quasi-nonexpansive mapping I, defined on a nonempty closed convex subset of a Banach space.