The Generalized \(\alpha\)-Nonexpansive Mappings and Related Convergence Theorems in Hyperbolic Spaces

Authors

  • Cholatis Suanoom Program of Mathematics, Faculty of Science and Technology, Kamphaengphet Rajabhat University, Kamphaengphet 62000
  • Kittikorn Sriwichai Program of Mathematics, Faculty of Science and Technology, Kamphaengphet Rajabhat University, Kamphaengphet 62000, Thailand; Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000
  • Chakkrid Klin-Eam Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000
  • Wongvisarut Khuangsatung Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi, Pathumthani, 12110

DOI:

https://doi.org/10.26713/jims.v11i1.1147

Keywords:

Fixed point set, Generalized \(\alpha\)-nonexpansive mappings, \(\Delta\)-convergence theorems and hyperbolic spaces

Abstract

In this paper, we propose and analyze a generalized \(\alpha\)-nonexpansive mappings on a nonempty subset of a hyperbolic space i.e., \begin{align*} \frac{1}{2}d(x,Tx)\leq d(x,y)\Longrightarrow d(Tx,Ty)\leq \alpha d(y,Tx)+\alpha d(x,Ty)+ (1-2\alpha)d(x,y), \end{align*} and prove \(\Delta\)-convergence theorems and convergence theorems for a generalized \(\alpha\)-nonexpansive mappings in a hyperbolic space.

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Published

2019-03-31
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How to Cite

Suanoom, C., Sriwichai, K., Klin-Eam, C., & Khuangsatung, W. (2019). The Generalized \(\alpha\)-Nonexpansive Mappings and Related Convergence Theorems in Hyperbolic Spaces. Journal of Informatics and Mathematical Sciences, 11(1), 1–17. https://doi.org/10.26713/jims.v11i1.1147

Issue

Vol. 11 No. 1 (2019)

Section

Research Articles

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