An Iterative Shrinking Metric f -Projection Method for Finding a Common Fixed Point of a Closed and Quasi-Strict f -Pseudocontraction and a Countable Family of Firmly Nonexpansive Mappings and Applications in Hilbert Spaces

Abstract

We create some new ideas of mappings called quasi-strict $f$-pseudocontractions. Moreover, we also find the significant inequality related to such mappings and firmly nonexpansive mappings within the framework of Hilbert spaces. By using the ideas of metric $f$-projection, we propose an iterative shrinking metric $f$-projection method for finding a common fixed point of a quasi-strict $f$-pseudocontraction and a countable family of firmly nonexpansive mappings. In addition, we provide some applications of the main theorem to find a common solution of fixed point problems and generalized mixed equilibrium problems as well as other related results.