In this paper, we prove some strong convergence results for a family of three generalized strongly Φ-pseudocontractive (accretive) mappings in Banach spaces. Our results are generalizations and improvements of convergence results obtained by several authors in literature. In particular, they generalize and improve the results of Olaleru and Mogbademu [17], Xue and Fan [22] which is in turn a co...

‎In this paper‎, ‎we prove some theorems related to properties of‎ ‎generalized symmetric hybrid mappings in Banach spaces‎. ‎Using Banach‎ ‎limits‎, ‎we prove a fixed point theorem for symmetric generalized‎ ‎hybrid mappings in Banach spaces‎. ‎Moreover‎, ‎we prove some weak‎ ‎convergence theorems for such mappings by using Ishikawa iteration‎ ‎method in a uniformly convex Banach space.

In this paper, we introduce a new algorithm for finding a common fixed point of a finite family of continuous pseudocontractive mappings which is a unique solution of some variational inequality problem and whose image under some bounded linear operator is a common solution of some system of equilibrium problems in a real Hilbert space. Our result generalize and improve some well-known results.

We introduce an iterative algorithm for finding a common element of the set of solutions of a system of mixed equilibrium problems, the set of solutions of a general system of variational inequalities for Lipschitz continuous and relaxed cocoercive mappings, the set of common fixed points for nonexpansive semigroups, and the set of common fixed points for an infinite family of strictly pseudoco...

We investigate the equivalence between the convergences of the Mann iteration method and the Ishikawa iteration method with errors for demicontinuous φ-strongly accretive operators in uniformly smooth Banach spaces. A related result deals with the equivalence of theMann iterationmethod and the Ishikawa iterationmethod for φ-pseudocontractive operators in nonempty closed convex subsets of unifor...

Let E be a real q-uniformly smooth Banach space, which is also uniformly convex (for example, Lp or p spaces, 1 < p <∞), and C be a nonempty bounded closed convex subset of E. Let T : C→ C be a k-strictly asymptotically pseudocontractive map with a nonempty fixed point set. A hybrid algorithm is constructed to approximate fixed points of such maps. Furthermore, strong convergence of the propose...

The purpose of this paper is to investigate the asymptotic behavior of algorithms for finding solutions for a certain class of variational inequalities V ID(C, I−f) involving nonexpansive type mappings in smooth Banach spaces. We study existence of solutions of variational inequalities V ID(C, I− f) when D is the set of solutions of zeros of accretive operators or the set of fixed points of non...

We prove strong convergence theorem for infinite family of uniformly L−Lipschitzian total quasi-φ-asymptotically nonexpansive multi-valued mappings using a generalized f−projection operator in a real uniformly convex and uniformly smooth Banach space. The result presented in this paper improve and unify important recent results announced by many authors.