ON THE EXISTENCE OF UNIQUE COMMON FIXED POINT OF TWO MAPPINGS IN A METRIC-LIKE SPACE
DOI:
https://doi.org/10.29121/ijetmr.v9.i12.2022.1256Keywords:
Metric-Like Space,, 0-Complete Metric-Like Space,, Common Fixed Point,, F-contraction.Abstract
The main objective of this article is to introduce a fixed-point result involving two mappings satisfying contraction in a metric-like space. The article has been designed in the following manner. In the first section the authors have mentioned some definitions and commonly used notations. In the second section, they have mentioned some fixed-point results. In the third section the authors have introduced their main result and in the last section, using these results, the authors have obtained some conditions that assure the existence of a common fixed point of a pair of mappings.
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Amini-Harandi, A. (2012). Metric-Like Spaces, Partial Metric Spaces and Fixed Points, Fixed Point Theory and Applications, 1(2012), 1-10. https://doi.org/10.1186/1687-1812-2012-204. DOI: https://doi.org/10.1186/1687-1812-2012-204
Banach, S. (1922). Sur Les Opérations Dans Les Ensembles Abstraits Et Leur Application Aux Equations Intégrales, Fundamenta Mathematicae, 3(1922), 133-181. https://doi.org/10.4064/fm-3-1-133-181. DOI: https://doi.org/10.4064/fm-3-1-133-181
Dhiman, D., Mishra, L.N. and Mishra, V.N. (2022). Solvability Of Some Non-Linear Functional Integral Equations Via Measures Of Noncompactness, Advanced Studies In Contemporary Mathematics, 32(2022), 157-171.
Fabiano, N., Nikolić, N., Fadail,,Z. M., Paunović, L. and Radenović, S. (2020). New Fixed Point Results on Αψl-Rational Contraction Mappings in Metric-Like Spaces, Filomat, 34(2020), 4627-4636. DOI: https://doi.org/10.2298/FIL2014627F
Fabijano, N., Parvaneh, V., Mirkovic, D., Paunovic, L. and Radenovic, S.(2020). On F- Contraction of Jungck-Ciric-Wardowski-Type Mappings in Metric Spaces, Cogent Mathematics and Statistics , 7(2020). https://doi.org/10.1080/25742558.2020.1792699. DOI: https://doi.org/10.1080/25742558.2020.1792699
Jungck. G. (1996). Common Fixed Points For Noncontinuous Nonself Maps on Nonmetric Spaces.
Karapınar, E. and Salimi, P. (2013).Dislocated Metric Space to Metric Spaces With Some Fixed Point Theorems, Fixed Point Theory and Applications, 1(2013), 1-19. https://doi.org/10.1186/1687-1812-2013-222. DOI: https://doi.org/10.1186/1687-1812-2013-222
Matthews, S. G. (1994). Partial Metric Topology, Annals of The New York Academy of Sciences, 728(1994), 183-197. https://doi.org/10.1111/j.1749-6632.1994.tb44144.x. DOI: https://doi.org/10.1111/j.1749-6632.1994.tb44144.x
Mishra, L.N., Gupta, A. and Mishra, V.N. (2021). Application of N-Tupled Fixed Points of Contractive Type Operators for Ulam-Hyers Stability, Palestine Journal of Mathematics, 10(2021), 349-372.
Mishra, L.N., Raiz, M., Rathour, L., and Mishra, V.N. (2022). Tauberian Theorems for Weighted Means of Double Sequences In Intuitionistic Fuzzy Normed Spaces, Yugoslav Journal of Operations Research, 32 (3), 377-388. https://doi.org/10.2298/YJOR210915005M. DOI: https://doi.org/10.2298/YJOR210915005M
Sanatee, A.G., Rathour, L., Mishra, V.N. and Dewangan, V. (2022). Some Fixed Point Theorems in Regular Modular Metric Spaces and Application to Caratheodory's Type Anti-Periodic Boundary Value Problem, The Journal Of Analysis. https://doi.org/10.1007/s41478-022-00469-z. DOI: https://doi.org/10.1007/s41478-022-00469-z
Shahi, P., Rathour, L., and Mishra, V.N (2022). Expansive Fixed Point Theorems for Tri-Similation Functions, The Journal of Engineering and Exact Sciences- Jcec, 8(2022), 14303-01e. DOI: https://doi.org/10.18540/jcecvl8iss3pp14303-01e
Sharma, N., Mishra, L.N., Mishra, V.N. and Pandey, S. (2020). Solution of Delay Differential Equation Via Nv1 Iteration Algorithm, European Journal of Pure and Applied Mathematics, 13(2020), 1110-1130. https://doi.org/10.29020/nybg.ejpam.v13i5.3756. DOI: https://doi.org/10.29020/nybg.ejpam.v13i5.3756
Shukla, S., Radenović, S. and Ćojbašić Rajić, V. (2013). Some Common Fixed Point Theorems in 0-Σ-Complete Metric-Like Spaces, Vietnam Journal of Mathematics, 41(2013), 341-352. https://doi.org/10.1007/s10013-013-0028-0. DOI: https://doi.org/10.1007/s10013-013-0028-0
Tamilvanan, K., Mishra, L.N. and Mishra, V.N., and Loganathan, K. (2020). Fuzzy Stability Results of Additive Functional Equation in Different Approaches, Annals of Communications In Mathematuics, 3(2020), 208-217.
Wardowski, D. (2012). Fixed Points of a New Type of Contractive Mappings in Complete Metric Spaces, Fixed Point Theory and Applications, 1(2012), 1-6. https://doi.org/10.1186/1687-1812-2012-94. DOI: https://doi.org/10.1186/1687-1812-2012-94
Wardowski, D. and Dung, N.V. (2014). Fixed Points of F-Weak Contractions on Complete Metric Spaces, Demonstratio Mathematica, 47(2014), 146-155. https://doi.org/10.2478/dema-2014-0012. DOI: https://doi.org/10.2478/dema-2014-0012
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