Properties of the generalized -projection operator and its applications in Banach spaces

Abstract: In this paper, we prove some properties of the generalized -projection operator in Banach spaces and show an interesting relation between the generalized -projection operator and the resolvent operator for the subdifferential of a proper, convex and lower semi-continuous functional in reflexive and smooth Banach spaces. Moreover, we prove that the generalized -projection operator is maximal monotone. As applications, we propose an iterative method of approximating solutions for a class of generalized variational inequalities and give a convergence result for the iterative method in uniformly convex and uniformly smooth Banach spaces. [Copyright &y& Elsevier]