The implicit midpoint rule of nonexpansive mappings and applications in uniformly smooth Banach spaces
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Aibinu, M. O.
Mewomo, O. T.
Journal of Non-Linear Sciences and Application
Let K be a nonempty closed convex subset of a Banach space E and T : K ! K be a nonexpansive mapping. Using a viscosity approximation method, we study the implicit midpoint rule of a nonexpansive mapping T. We establish a strong convergence theorem for an iterative algorithm in the framework of uniformly smooth Banach spaces and apply our result to obtain the solutions of an accretive mapping and a variational inequality problem. The numerical example which compares the rates of convergence shows that the iterative algorithm is the most efficient. Our result is unique and the method of proof is of independent interest.
Viscosity technique , Banach space E , Convergence theorem , Variational inequality problem , Research Subject Categories::MATHEMATICS
Aibinu, M. O.; Pillay, P.; Olaleru, J.O and Mewomo, O. T. (2018). The implicit midpoint rule of nonexpansive mappings and applications in uniformly smooth Banach spaces. J. Nonlinear Sci. Appl., 11 , 1374–1391.