On generalized convex contractions of type-2 in b-metric and 2-metric spaces
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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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ISRP Style
M. S. Khan, Y. M. Singh, G. Maniu, M. Postolache, On generalized convex contractions of type-2 in b-metric and 2-metric spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 6, 2902--2913
AMA Style
Khan M. S., Singh Y. M., Maniu G., Postolache M., On generalized convex contractions of type-2 in b-metric and 2-metric spaces. J. Nonlinear Sci. Appl. (2017); 10(6):2902--2913
Chicago/Turabian Style
Khan, M. S., Singh, Y. M., Maniu, G., Postolache, M.. "On generalized convex contractions of type-2 in b-metric and 2-metric spaces." Journal of Nonlinear Sciences and Applications, 10, no. 6 (2017): 2902--2913
Keywords
- Approximate fixed point
- fixed point
- convex contraction
- asymptotic regular
- \(\alpha\)-admissible
- b-metric and 2-metric spaces.
MSC
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