Two algorithms for solving mixed equilibrium problems and fixed point problems in Hilbert spaces

2021 ◽  
Author(s):  
Mohammad Farid
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Fixed Point Problems ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium

scholarly journals An Iterative Shrinking Projection Method for Solving Fixed Point Problems of Closed andϕ-Quasi-Strict Pseudocontractions along with Generalized Mixed Equilibrium Problems in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Kasamsuk Ungchittrakool
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Projection Method ◽  
Equilibrium Problems ◽  
Fixed Point Problems ◽  
Generalized Mixed Equilibrium Problems ◽  
Shrinking Projection Method ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

We provide some new type of mappings associated with pseudocontractions by introducing some actual examples in smooth and strictly convex Banach spaces. Moreover, we also find the significant inequality related to the mappings mentioned in the paper and the mappings defined from generalized mixed equilibrium problems on Banach spaces. We propose an iterative shrinking projection method for finding a common solution of generalized mixed equilibrium problems and fixed point problems of closed andϕ-quasi-strict pseudo-contractions. Our results hold in reflexive, strictly convex, and smooth Banach spaces with the property (K). The results of this paper improve and extend the corresponding results of Zhou and Gao (2010) and many others.

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