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

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) -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.