Fixed Point Theorems on ℵ-Extended Fuzzy Bipolar b-Metric Spaces
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Abstract
In this paper, we introduce the context of ℵ-Extended fuzzy bipolar b-metric space and prove fixed point theorem. Some of the well-known results in the literature are expanded and generalized by our research. Additionally, we presented applications to integral equation and fractional differential equation.
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References
- B. Schweizer, A. Sklar, Statistical Metric Spaces, Pac. J. Math. 10 (1960), 313–334.
- L.A. Zadeh, Fuzzy Sets, Inf. Control 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X.
- I. Kramosil, J. Michalek, Fuzzy Metric and Statistical Metric Spaces, Kybernetica 11 (1975), 326–334. http://dml.cz/dmlcz/125556.
- A. George, P. Veeramani, On Some Results in Fuzzy Metric Spaces, Fuzzy Sets Syst. 64 (1994), 395–399. https://doi.org/10.1016/0165-0114(94)90162-7.
- M. Grabiec, Fixed Points in Fuzzy Metric Spaces, Fuzzy Sets Syst. 27 (1988), 385–389. https://doi.org/10.1016/0165-0114(88)90064-4.
- V. Gregori, A. Sapena, On Fixed-Point Theorems in Fuzzy Metric Spaces, Fuzzy Sets Syst. 125 (2002), 245–252. https://doi.org/10.1016/S0165-0114(00)00088-9.
- A. Mutlu, U. Gürdal, Bipolar Metric Spaces and Some Fixed Point Theorems, J. Nonlinear Sci. Appl. 09 (2016), 5362–5373. https://doi.org/10.22436/jnsa.009.09.05.
- A. Bartwal, R.C. Dimri, G. Prasad, Some Fixed Point Theorems in Fuzzy Bipolar Metric Spaces, J. Nonlinear Sci. Appl. 13 (2020), 196–204. https://doi.org/10.22436/jnsa.013.04.04.
- M.S. Sezen, Controlled Fuzzy Metric Spaces and Some Related Fixed Point Results, Numer. Methods Partial Differ. Equ. 37 (2021), 583–593. https://doi.org/10.1002/num.22541.
- G. Mani, A.J. Gnanaprakasam, L. Guran, R. George, Z.D. Mitrovi´c, Some Results in Fuzzy B-Metric Space with b-Triangular Property and Applications to Fredholm Integral Equations and Dynamic Programming, Mathematics 11 (2023), 4101. https://doi.org/10.3390/math11194101.
- G. Mani, A.J. Gnanaprakasam, O. Ege, A. Aloqaily, N. Mlaiki, Fixed Point Results in C ∗ -Algebra-Valued Partial b-Metric Spaces with Related Application, Mathematics 11 (2023), 1158. https://doi.org/10.3390/math11051158.
- G. Mani, S. Haque, A.J. Gnanaprakasam, O. Ege, N. Mlaiki, The Study of Bicomplex-Valued Controlled Metric Spaces with Applications to Fractional Differential Equations, Mathematics 11 (2023), 2742. https://doi.org/10.3390/math11122742.
- A.J. Gnanaprakasam, G. Mani, O. Ege, A. Aloqaily, N. Mlaiki, New Fixed Point Results in Orthogonal B-Metric Spaces with Related Applications, Mathematics 11 (2023), 677. https://doi.org/10.3390/math11030677.
- G. Nallaselli, A.J. Gnanaprakasam, G. Mani, Z.D. Mitrovi´c, A. Aloqaily, N. Mlaiki, Integral Equation via Fixed Point Theorems on a New Type of Convex Contraction in B-Metric and 2-Metric Spaces, Mathematics 11 (2023), 344. https://doi.org/10.3390/math11020344.
- B. Ramalingam, O. Ege, A. Aloqaily, N. Mlaiki, Fixed-Point Theorems on Fuzzy Bipolar b-Metric Spaces, Symmetry 15 (2023), 1831. https://doi.org/10.3390/sym15101831.
- M. Younis, A.A.N. Abdou, Novel Fuzzy Contractions and Applications to Engineering Science, Fractal Fract. 8 (2023), 28. https://doi.org/10.3390/fractalfract8010028.
- S.Zhang, Positive solutions for boundary-value problems of nonlinear fractional differential equations, Electron. J. Differ. Equ. 2006 (2006), 36.
- I. Beg, A.J. Gnanaprakasam, G. M, Common Coupled Fixed Point Theorem on Fuzzy Bipolar Metric Spaces, Int. J. Nonlinear Anal. Appl. 14 (2023), 77–85. https://doi.org/10.22075/ijnaa.2023.27787.3712.