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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 and ϕ-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

abstract and applied analysis

An Iterative Shrinking Projection Method for Solving Fixed Point Problems of Closed and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>ϕ</mml:mi></mml:mrow></mml:math>-Quasi-Strict Pseudocontractions along with Generalized Mixed Equilibrium Problems in Banach Spaces

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