* Correspondence: [email protected] School of Science, South West University of Science and Technology, Mianyang, Sichuan 621010, China Abstract The purpose of this is to introduce and study total asymptotically strict pseudocontractive semigroup, asymptotically strict pseudocontractive semigroup etc. the strong convergence theorems of the explicit iteration process for the new semigroups ...

The purpose of this paper is first to introduce the concept of total quasi-φ-asymptotically nonexpansive mapping which contains many kinds of mappings as its special cases and then to use a hybrid algorithm to introduce a new iterative scheme for finding a common element of the set of solutions for a system of generalized mixed equilibrium problems and the set of common fixed points for a count...

In this paper, we consider an iteration process for approximating common fixed points of two asymptotically quasinonexpansive mappings and we prove some strong and weak convergence theorems for such mappings in uniformly convex Banach spaces. Keywords—Asypmtotically quasi-nonexpansive mappings, Common fixed point, Strong and weak convergence, Iteration process.

The purpose of this article is to discuss a modified Halpern-type iteration algorithm for a countable family of uniformly totally quasi- -asymptotically nonexpansive multi-valued mappings and establish some strong convergence theorems under certain conditions. We utilize the theorems to study a modified Halpern-type iterative algorithm for a system of equilibrium problems. The results improve ...

This article investigates some properties of quasi-cyclic and cyclic Jungck modified TS-iterative schemes in complete metric spaces and Banach spaces. In particular, properties of convergence of distances and sequences associated with the self-mappings which define the Jungck modified TS-iterative procedures are studied as well as some properties concerning the convergence of the solution to co...

zero point problems of the sum of two monotone mappings and fixed point problems of a strictly pseudocontractive mapping are investigated‎. ‎a strong convergence theorem for the common solutions of the problems is established in the framework of hilbert spaces‎.