Strong Convergence of a New Three Step Iterative Scheme in Banach Spaces

A three-step iterative scheme for solving nonlinear φ-strongly accretive operator equations in Banach spaces

Convergence theorems of multi-step iterative algorithm with errors for generalized asymptotically quasi-nonexpansive mappings in Banach spaces

The purpose of this paper is to study and give the necessary andsufficient condition of strong convergence of the multi-step iterative algorithmwith errors for a finite family of generalized asymptotically quasi-nonexpansivemappings to converge to common fixed points in Banach spaces. Our resultsextend and improve some recent results in the literature (see, e.g. [2, 3, 5, 6, 7, 8,11, 14, 19]).

Strong Convergence of a Multi-step Iterative Process for Relatively Quasi-nonexpansive Multivalued Mappings and Equilibrium Problem in Banach Spaces

Let E be a real Banach space with norm ∥.∥ and let J be the normalized duality mapping from E into 2E ∗ given by Jx = {x∗ ∈ E∗ : ⟨x, x∗⟩ = ∥x∥∥x∗∥, ∥x∥ = ∥x∗∥} for all x ∈ E, where E∗ denotes the dual space of E and ⟨., .⟩ denotes the generalized duality pairing between E and E∗. A Banach space E is said to be strictly convex if ∥ 2 ∥ < 1 for all x, y ∈ E with ∥x∥ = ∥y∥ = 1 and x ̸= y. It is sai...

Strong Convergence of the Iterations of Quasi $phi$-nonexpansive Mappings and its Applications in Banach Spaces

In this paper, we study the iterations of quasi $phi$-nonexpansive mappings and its applications in Banach spaces. At the first, we prove strong convergence of the sequence generated by the hybrid proximal point method to a common fixed point of a family of quasi $phi$-nonexpansive mappings.  Then, we give  applications of our main results in equilibrium problems.

Convergence results‎: ‎A new type iteration scheme for two asymptotically nonexpansive mappings in uniformly convex Banach spaces

‎In this article‎, ‎we introduce a new type iterative scheme for‎ ‎approximating common fixed points of two asymptotically‎ ‎nonexpansive mappings is defined‎, ‎and weak and strong convergence‎ ‎theorem are proved for the new iterative scheme in a uniformly‎ ‎convex Banach space‎. ‎The results obtained in this article‎ ‎represent an extension as well as refinement of previous known‎ ‎resu...