It is defined a class of generalized nonexpansive mappings, which properly contains those by Suzuki in 2008, and that preserves some its fixed point results.

The aim of this paper is to investigate hybrid algorithm for a common zero point of the sum of two monotone operators which is also a fixed point of a family of countable quasi-nonexpansive mappings. We point out two incorrect proof in paper (Hecai in Fixed Point Theory Appl 2013:11, 2013). Further, we modify and generalize the results of Hecai's paper, in which only a quasi-nonexpansive mappin...

In this paper,we establish fixed points theorems in Banach space using Mann Iteration for nonexpansive and asymtotically nonexpansive mappings . Iteration scheme is defined by (2.1) and (2.2). We extended the work of Mann.

We introduce a new iterative scheme by shrinking projection method for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of common solutions of variational inclusion problems with set-valued maximal monotone mappings and inverse-strongly monotone mappings, the set of solutions of fixed points for nonexpansive semigroups, and the set of common fi...

We introduce new iterative algorithms by hybrid method for finding a common element of the set of solutions of fixed points of infinite family of nonexpansive mappings, the set of common solutions of generalized mixed equilibrium problems, and the set of common solutions of the variational inequality with inverse-strongly monotone mappings in a real Hilbert space. We prove the strong convergenc...

In this paper, we shall introduce an iterative algorithm by multi-step implicit hybrid steepestdescent method for finding a common element of the set of solutions of a finite family of generalized mixed equilibrium problems, the set of solutions of a finite family of variational inequalities for inverse strongly monotone mappings and the set of fixed points of a countable family of nonexpansive...

Abstract In this paper, we suggest and analyze an iterative algorithm to approximate a common solution of hierarchical fixed point problem for nonexpansive mappings, system variational inequalities, split equilibrium in Hilbert spaces. Under some suitable conditions imposed on the sequences parameters, prove that sequence generated by proposed method converges strongly element set these three k...