An Iterative Shrinking Generalized $f$-Projection Method for $G$-Quasi-Strict Pseudo-Contractions in Banach Spaces

Kasamsuk Ungchittrakool, Narin Petrot, Apisit Jarernsuk

Abstract

The purposes of this paper are to study the new type of mappings called $G$-quasi-strict pseudo-contractions and to create some iterative projection techniques to find some fixed points of the mappings. Moreover, we also find the significant inequality related to such mappings in the framework of Banach spaces. By using the ideas of the generalized $f$-projection, we propose an iterative shrinking generalized $f$-projection method for finding a fixed point of $G$-quasi-strict pseudo-contractions. The results of this paper improve and extend the corresponding results of  Zhou and Gao [H. Zhou, E. Gao, An iterative method of fixed points for closed and quasi-strict pseudocontractions in Banach spaces, J. Appl. Math. Comput. 33 (2010) 227-237.] as well as other related results.