We prove strong convergence theorems for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a hemirelatively nonexpansive mapping in a Banach space by using monotone hybrid iteration method. By using these results, we obtain new convergence results for resolvents of maximal monotone operators and hemirelatively nonexpansive mappings in a Ban...

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.

It is shown that any A-firmly, 0 < A < 1 , nonexpansive mapping T: C —> C has a fixed point in C whenever C is a finite union of nonempty, bounded, closed convex subsets of a uniformly convex Banach space. Let C be a nonempty subset of a Banach space X, and let X £ (0, 1). Then a mapping T: C —> X is said to be X-firmly nonexpansive if (1) \\Tx Ty\\ < ||(1 X)(x y)+X(Tx Ty)\\ for all x, y £ C. I...

In this paper, we first prove a weak convergence theorem by Mann’s iteration for a commutative family of positively homogeneous nonexpansive mappings in a Banach space. Next, using the shrinking projection method defined by Takahashi, Takeuchi and Kubota, we prove a strong convergence theorem for such a family of the mappings. These results are new even if the mappings are linear and contractive.

In this article, we consider an implicit iterative scheme for two asymptotically quasi-I-nonexpansive mappingsS1, S2 and two asymptotically quasi-nonexpansive mapping I1, I2 in Banach space. We obtain convergence results for considered iteration to common fixed point of two asymptotically quasi-I-nonexpansive mappings, asymptotically quasi-nonexpansive mapping and equilibrium problem in frame w...

The main purpose of this paper is to give weak and strong convergence theorems of a new three-step iterative scheme for asymptotically nonexpansive mappings in Banach spaces and we also give several weak and strong convergence theorems of the three-step iterative scheme with errors for asymptotically nonexpansive mappings in Banach spaces. Mann-type and Ishikawa -type iterations are included by...

in this paper, we establish an existence result of the solution for an generalized strong vector variational inequality already considered in the literature and as applications we obtain a new coincidence point theorem in hilbert spaces.

Throughout this paper, let H be a real Hilbert space with inner product 〈·,·〉 and norm ‖ · ‖. Let C be a nonempty closed convex subset of H , we denote by PC(·) the metric projection from H onto C. It is known that z = PC(x) is equivalent to 〈z− y,x− z〉 ≥ 0 for every y ∈ C. Recall that T : C → C is nonexpansive if ‖Tx− Ty‖ ≤ ‖x− y‖ for all x, y ∈ C. A point x ∈ C is a fixed point of T provided ...

We prove Browder’s type strong convergence theorems for infinite families of nonexpansive mappings. One of our main results is the following: let C be a bounded closed convex subset of a uniformly smooth Banach space E. Let {Tn : n ∈ N} be an infinite family of commuting nonexpansive mappings on C. Let {αn} and {tn} be sequences in (0,1/2) satisfying limn tn = limn αn/t n = 0 for ∈ N. Fix u ∈ C...