Fixed point and its iteration theorems of new mappings in Banach spaces (Study on Nonlinear Analysis and Convex Analysis)

Abstract

In a Hilbert space, concepts of attractive point and acute point studied by many researchers. Moreover, these concepts extended to Banach space. In this paper, we introduce a new class of mappings on Banach space corresponding to the class of all widely more generalized hybrid mappings on Hilbert space. Moreover, we introduce some extensions of acute point and prove some acute point theorems and some extensions of weak convergence theorems.