A Study On The Well-pose Of Solutions For A Class Of Variational Inequality Problem In Banach Spaces

Variational inequality is an important part of nonlinear analysis theory, andvariational inclusion is an important branch of variational inequality. In this paper, thesolution of variational inequality problem is studied in Banach spaces. First, thevariational inclusion problem, which is k time strongly accretive, is improved. Theconditions "smooth Banach spaces" is weakened to "reflexive Banach spaces." Theauthor use general duality principle and fixed point theory to prove that the Existenceand Uniqueness of Solutions for the class of Variational Inclusion Problem. Themathematical induction and norm scaling principle are used to prove the convergence ofIshikawa iterative. Secondly, the τ Lipschitz strongly accretive Variational InclusionProblem is put forward, as well as the related concepts. The result of this papergeneralized the Variational Inequality Problem in many aspects. The existence,uniqueness and convergence of Ishikawa iterative sequence for the Variational InclusionProblem are proved,and a number of related inferences are introduced. In short, thispaper’s result improve and extend the Variational Inequality Problem of the relatedresults in many aspects.