Convergence of Iterative Algorithms for Continuous Pseudocontractive Mappings

Abstract

In this paper, we prove convergence of a path for a convex
combination of a pseudocontractive type of operators in a real
reflexive Banach space having a weakly continuous
 duality mapping $J_{\varphi}$ with gauge function $\varphi$. Using of path convergency, we establish
 strong convergence of an implicit iterative algorithm for
 pseudocontractive mapping combined with strongly pseudocontractive mapping in the same Banach space.