On \((\alpha, p)\)-convex contraction and asymptotic regularity

Volume 18, Issue 2, pp 132--145

Publication Date: 2018-01-12

http://dx.doi.org/10.22436/jmcs.018.02.01

Authors

M. S. Khan - Department of Mathematics and Statistics, Sultan Qaboos University, P. O. Box 36, PCode 123 Al-Khod, Muscat, Sultanate of Oman, Oman
Y. Mahendra Singh - Department of Humanities and Basic Sciences, Manipur Institute of Technology, Takyelpat-795001, India
Georgeta Maniu - Department of Computer Science, Information Technology, Mathematics and Physics, Petroleum-Gas University of Ploiesti, Bucuresti Bvd., No. 39, 100680 Ploiesti, Romania
Mihai Postolache - China Medical University, Taichung, Taiwan

Abstract

In this paper, we present the notions of \((\alpha, p)\)-convex contraction (resp. \((\alpha, p)\)-contraction) and asymptotically \(T^2\)-regular (resp. \((T, T^2)\)-regular) sequences, and prove fixed point theorems in the setting of metric spaces.

Keywords

Approximate fixed point, fixed point, \((\alpha, p)\)-convex contraction, asymptotically regular sequence, asymptotically \(T\) (resp. \(T^2\) and \((T, T^2)\))-regular sequences

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