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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 ofHilbert spaces. By using the ideas of metric f-projection, we propose an iterative shrinking metric f-projection methodfor finding a common fixed point of a quasi-strict f-pseudocontraction and a countable family of firmly nonexpansivemappings. In addition, we provide some applications of the main theorem to find a common solution of fixed pointproblems and generalized mixed equilibrium problems as well as other related results

abstract and applied analysis

An Iterative Shrinking Metricf-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