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.
