In this paper, we establish a fixed point theorem for two mappings under a contraction condition in b2-metric space, and this theorem is related to a Suzuki-type of contraction.
References
[1]
Banach, S. (1922) Sur les opérations dans les ensembles abtraits et leur applications aux équations intégrales. Fundamenta Mathematicae, 3, 133-181. https://doi.org/10.4064/fm-3-1-133-181
[2]
Ekeland, I. (1974) On the Variational Principle. Journal of Mathematical Analysis and Applications, 47, 324-353. https://doi.org/10.1016/0022-247X(74)90025-0
[3]
Meir, A. and Keeler, E. (1969) A Theorem on Contraction Mappings. Journal of Mathematical Analysis and Applications, 28, 326-329. https://doi.org/10.1016/0022-247X(69)90031-6
Caristi, J. (1976) Fixed Point Theorems for Mappings Satisfying Inwardness Conditions. Transactions of the American Mathematical Society, 215, 241-251. https://doi.org/10.1090/S0002-9947-1976-0394329-4
[6]
Caristi, J. and Kirk, W.A. (1975) Geometric Fixed Point Theory and Inwardness Conditions. Lecture Notes in Mathematics, 499, 74-83. https://doi.org/10.1007/BFb0081133
[7]
Subrahmanyam, P.V. (1974) Remarks on Some Fixed Point Theorems Related to Banach’s Contraction Principle. Electronic Journal of Mathematical and Physical Sciences, 8, 445-457.
[8]
Suzuki, T. (2004) Generalized Distance and Existence Theorems in Complete Metric Spaces. Journal of Mathematical Analysis and Applications, 253, 440-458. https://doi.org/10.1006/jmaa.2000.7151
[9]
Mustafa, Z., Parvaech, V., Roshan, J.R. and Kadelburg, Z. (2014) b2-Metric Spaces and Some Fixed Point Theorems. Fixed Point Theory and Applications, 2014, Article Number: 144. https://doi.org/10.1186/1687-1812-2014-144
[10]
Fadail, Z.M., Ahmad, A.G.B., Ozturk, V. and Radenovi？, S. (2015) Some Remarks on Fixed Point Results of b2-Metric Spaces. Far East Journal of Mathematical Sciences, 97, 533-548. https://doi.org/10.17654/FJMSJul2015_533_548
