The Convergence Results for an AK-Generalized Nonexpansive Mapping in Hilbert Spaces

Cholatis Suanoom, Wongvisarut Khuangsatung

Abstract

In this paper, we introduce a new class of nonexpansive type of mapping namely, AK-generalized nonexpansive mapping, which is more general than an $\alpha$-nonexpansive mapping. Moreover, we obtain convergence results  of the  viscosity approximation method  for an AK-generalized nonexpansive semigroups under some assumptions  in Hilbert spaces. Furthermore, we prove  a strong convergence theorem  for a family of AK-generalized nonexpansive mapping in Hilbert spaces.