The generalized viscosity implicit rule of nonexpansive semigroup in Banach spaces
- Department of Mathematics, Faculty of Liberal Arts, Rajamangala University of Technology Rattanakosin, Nakhon Pathom 73170, Thailand.
- Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand.
- 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.
- Nonexpansive semigroup
- fixed point
- generalized viscosity
- Banach space
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