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
Kasamsuk Ungchittrakool, Duangkamon Kumtaeng · Abstract and Applied Analysis · 2013
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.