Strong Convergence of the Iterations of Quasi \phi-nonexpansive Mappings and its Applications in Banach Spaces

In this paper, we study the iterations of quasi \phi-nonexpansive mappings and its applications in Banach spaces. At the first, we prove strong convergence of the sequence generated by the hybrid proximal point method to a common fixed point of a family of quasi \phi-nonexpansive mappings.  Then, we give  applications of our main results in equilibrium problems.

Keywords:

Demiclosed‎ , ‎equilibrium problem‎ , ‎fixed point‎ , ‎hybrid projection‎ , ‎quasi nonexpansive mapping‎ , Resolvent