The Over-Relaxed <inline-formula> <graphic file="1687-1812-2011-840978-i1.gif"/></inline-formula>-Proximal Point Algorithm for General Nonlinear Mixed Set-Valued Inclusion Framework

Abstract

The purpose of this paper is (1) a general nonlinear mixed set-valued inclusion framework for the over-relaxed -proximal point algorithm based on the ( , )-accretive mapping is introduced, and (2) it is applied to the approximation solvability of a general class of inclusions problems using the generalized resolvent operator technique due to Lan-Cho-Verma, and the convergence of iterative sequences generated by the algorithm is discussed in -uniformly smooth Banach spaces. The results presented in the paper improve and extend some known results in the literature.