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


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


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.