On generalized convex contractions of type-2 in b-metric and 2-metric spaces

Volume 10, Issue 6, pp 2902--2913 http://dx.doi.org/10.22436/jnsa.010.06.05

Publication Date: June 25, 2017 Submission Date: April 09, 2017

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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. Y. M. Singh - Department of Humanities and Basic Sciences, Manipur Institute of Technology, Takyelpat–795001, India. G. Maniu - Department of Computer Science, Information Technology, Mathematics and Physics, , Petroleum-Gas University of Ploieşti, Bucureşti Bvd., No. 39, 100680 Ploieşti, Romania. M. Postolache - China Medical University, No. 91, Hsueh-Shih Road, Taichung, Taiwan. - Department of Mathematics & Informatics, University ”Politehnica” of Bucharest, Splaiul Independentei 313, Bucharest 060042, Romania.

Abstract

In this paper, we present the notion of generalized convex contraction mapping of type-2, which includes the generalized convex contraction (resp. generalized convex contraction of order-2) of Miandaragh et al. [M. A. Miandaragh, M. Postolache, S. Rezapour, Fixed Point Theory Appl., 2013 (2013), 8 pages] and the convex contraction mapping of type-2 of Istrăţescu[V. I. Istrăţescu, I, Libertas Math., 1 (1981), 151–163]. Utilizing this class of mappings, we establish approximate fixed point and fixed point theorems in the setting of b-metric and 2-metric spaces.

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Keywords

• Approximate fixed point
• fixed point
• convex contraction
• asymptotic regular
• \(\alpha\)-admissible
• b-metric and 2-metric spaces.

MSC

•  47H10
•  54H25

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