We create some new ideas of mappings called quasi-strict -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 -projection, we propose an iterative shrinking metric -projection method for finding a common fixed point of a quasi-strict -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.
"An Iterative Shrinking Metric -Projection Method for Finding a Common Fixed Point of a Closed and Quasi-Strict-Pseudocontraction and a Countable Family of Firmly Nonexpansive Mappings and Applications in Hilbert Spaces." Abstr. Appl. Anal. 2013 1 - 11, 2013. https://doi.org/10.1155/2013/589282