Constructing an Iterative algorithm for Variational Inequality Problem of a Finite Family of Pseudomonotone Mappings in Banach Spaces

Abstract

In this thesis we constructed an iterative scheme for approximat ing a common solution of a variational inequality problem of a nite family of pseudo monotone mappings in Banach spaces and proved a strong convergence of a sequence generated by proposed algorithm to a common solution of for a variational inequality problem of a nite family of pseudo monotone mappings in Banach spaces. Finally, pre sented an applications of our main results to approximating a com mon point of a nite family of convex functions in Banach spaces. Our results improved and generalized most of the results that have been proved for this important class of nonlinear mappings. In par ticular, Theorem 5.1.4 extend the results of H. Iiduka et al, (2004), N. Nadezhkina and W. Takahashi, (2006), A. Tad and W. Takahashi, (2007), W. Takahashi and M. Toyoda, (2003) and Y. Zhanga and Q. Yuanb, (2016) from real Hilbert spaces to real re exive Banach spaces. Moreover, Theorem 5.1.5 extends Theorem 3.1 of Tufa and Zegeye, (2015) and Wega and Zegeye, (2021) from Lipschitz mono tone mappings variational inequality to continuous pseudomonotone mappings variational inequality in real re exive Banach spaces.