Fixed points of weakly K-nonexpansive mappings and a stability result for fixed point iterative process with an application

Abstract

Abstract In this article, we introduce a new type of non-expansive mapping, namely weakly K-nonexpansive mapping, which is weaker than non-expansiveness and stronger than quasi-nonexpansiveness. We prove some weak and strong convergence results using weakly K-nonexpansive mappings. Also, we define weakly ( α , K ) $(\alpha ,K)$ -nonexpansive mapping and using it prove one stability result for JF-iterative process. Some prominent examples are presented illustrating the facts. A numerical example is given to compare the convergence behavior of some known iterative algorithms for weakly K-nonexpansive mappings. Moreover, we show by example that the class of α-nonexpansive mappings due to Aoyama and Kohsaka and the class of generalized α-nonexpansive mappings due to Pant and Shukla are independent. Finally, our fixed point theorem is applied to obtain a solution of a nonlinear fractional differential equation.

Keywords

• Weakly K-nonexpansive and weakly ( α , K ) $(\alpha ,K)$ -nonexpansive mappings
• Suzuki’s Condition (C)
• Generalized α-nonexpansive mapping
• Strong and weak convergence theorems
• Stability result
• JF-iterative scheme