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

Volume 18, Issue 2, pp 132--145 Publication Date: January 12, 2018       Article History
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### 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

•  47H10
•  54H25

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