The generalized viscosity implicit rule of nonexpansive semigroup in Banach spaces

Volume 11, Issue 6, pp 746--761 Publication Date: April 13, 2018       Article History


Chaichana Jaiboon - Department of Mathematics, Faculty of Liberal Arts, Rajamangala University of Technology Rattanakosin, Nakhon Pathom 73170, Thailand. Somyot Plubtieng - Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand. Phayap Katchang - Rajamangala University of Technology Lanna Tak, Division of Mathematics, Faculty of Science and Agricultural Technology, Rajamangala University of Technology Lanna Tak, Tak 63000, Thailand, Tak 63000, Thailand.


In this research, we focus on a common fixed point problem of a nonexpansive semigroup with the generalized viscosity methods for implicit iterative algorithms. Our main objective is to construct the new strong convergence theorems under certain appropriate conditions in uniformly convex and uniformly smooth Banach spaces. Specifically, the main results make a contribution to the implicit midpoint theorems. The findings for theorems in Hilbert spaces and the other forms of a nonexpansive semigroup can be used in several practical purposes. Finally, a numerical example in 3 dimensions is provided to support our main results.