A New Iterative Scheme of Modified Mann Iteration in Banach Space

Some results on a modified Mann iterative scheme in a reflexive Banach space

Weak Convergence of Mann Iteration for a Hybrid Pair of Mappings in a Banach Space

We prove the weak convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multivalued f nonexpansive mapping T in Banach space E. Keywords—Common fixed point, Mann iteration, Multivalued mapping, weak convergence.

A modified Mann iterative scheme for a sequence of‎ ‎nonexpansive mappings and a monotone mapping with applications

‎In a real Hilbert space‎, ‎an iterative scheme is considered to‎ ‎obtain strong convergence which is an essential tool to find a‎ ‎common fixed point for a countable family of nonexpansive mappings‎ ‎and the solution of a variational inequality problem governed by a‎ ‎monotone mapping‎. ‎In this paper‎, ‎we give a procedure which results‎ ‎in developing Shehu's result to solve equilibrium prob...

Strong and Weak Convergence of Modified Mann Iteration for New Resolvents of Maximal Monotone Operators in Banach Spaces

and Applied Analysis 3 2. Preliminaries Let E be a real Banach space with dual space E∗. When {xn} is a sequence in E, we denote strong convergence of {xn} to x ∈ E by xn → x and weak convergence by xn ⇀ x, respectively. As usual, we denote the duality pairing of E∗ by 〈x, x∗〉, when x∗ ∈ E∗ and x ∈ E, and the closed unit ball by UE, and denote by R and N the set of all real numbers and the set ...

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...