The generalized viscosity implicit rule of nonexpansive semigroup in Banach spaces

Volume 11, Issue 6, pp 746--761 http://dx.doi.org/10.22436/jnsa.011.06.02

Publication Date: April 13, 2018 Submission Date: June 29, 2017 Revision Date: March 22, 2018 Accteptance Date: March 22, 2018

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Authors

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.

Abstract

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.

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ISRP Style

Chaichana Jaiboon, Somyot Plubtieng, Phayap Katchang, The generalized viscosity implicit rule of nonexpansive semigroup in Banach spaces, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 6, 746--761

AMA Style

Jaiboon Chaichana, Plubtieng Somyot, Katchang Phayap, The generalized viscosity implicit rule of nonexpansive semigroup in Banach spaces. J. Nonlinear Sci. Appl. (2018); 11(6):746--761

Chicago/Turabian Style

Jaiboon, Chaichana, Plubtieng, Somyot, Katchang, Phayap. "The generalized viscosity implicit rule of nonexpansive semigroup in Banach spaces." Journal of Nonlinear Sciences and Applications, 11, no. 6 (2018): 746--761

Keywords

Nonexpansive semigroup
fixed point
generalized viscosity
implicit
Banach space

MSC

47H10
47H20
47J20

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