a new iterative method for solving constrained minimization, variational inequality and split feasibility problems in the framework of banach spaces

In this paper, we introduce a new type of modifiedgeneralized α-nonexpansive mapping and establish some fixed pointproperties and demiclosedness principle for this class of mappingsin the framework of uniformly convex banach spaces. we furtherpropose a new iterative method for approximating a common fixedpoint of two modified generalized α-nonexpansive mappings andpresent some weak and strong convergence theorems for these mappings in uniformly convex banach spaces. in addition, we apply ourresult to solve a convex-constrained minimization problem, variational inequality and split feasibility problem and present somenumerical experiments in infinite dimensional spaces to establishthe applicability and efficiency of our proposed algorithm. the obtained results in this paper improve and extend some related resultsin the literature.