We define a viscosity method for continuous pseudocontractive mappings defined on closed and convex subsets of reflexive Banach spaces with a uniformly Gâteaux differentiable norm. We prove the convergence of these schemes improving the main theorems in the work by Y. Yao et al.

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 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.

This paper is concerned with an ergodic theorem for asymptotically nonexpansive mappings in the intermediate sense in Banach spaces.