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

Abstract EN

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.