Solving Integral Equation via Fixed Point Theorem on Neutrosophic Bipolar Cone Metric Spaces
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Abstract
In this article, we introduce the notion of neutrosophic bipolar cone metric space and prove fixed point theorems. The authors demonstrate various satisfying contraction mapping results using non-trivial examples. Finally, we prove existence and uniqueness results of the integral equation to strengthen our obtained result.
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References
- A. Aloqaily, Systems of Linear Equations in Generalized b-Metric Spaces, Int. J. Anal. Appl. 22 (2024), 227. https://doi.org/10.28924/2291-8639-22-2024-227.
- W. Shatanawi, T.A.M. Shatnawi, New Fixed Point Results in Controlled Metric Type Spaces Based on New Contractive Conditions, AIMS Math. 8 (2023), 9314–9330. https://doi.org/10.3934/math.2023468.
- A. Rezazgui, A.A. Tallafha, W. Shatanawi, Common Fixed Point Results via $ mathcal{A}_{vartheta} $-$alpha$-Contractions with a Pair and Two Pairs of Self-Mappings in the Frame of an Extended Quasi $b$-Metric Space, AIMS Math. 8 (2023), 7225–7241. https://doi.org/10.3934/math.2023363.
- M. Joshi, A. Tomar, T. Abdeljawad, On Fixed Points, Their Geometry and Application to Satellite Web Coupling Problem in $mathcal{S}$-Metric Spaces, AIMS Math. 8 (2023), 4407–4441. https://doi.org/10.3934/math.2023220.
- L. Zadeh, Fuzzy Sets, Inf. Control. 8 (1965), 338–353. https://doi.org/10.1016/s0019-9958(65)90241-x.
- B. Schweizer, A. Sklar, Statistical Metric Spaces, Pac. J. Math. 10 (1960), 313–334. https://doi.org/10.2140/pjm.1960.10.313.
- I. Kramosil, J. Michalek, Fuzzy Metric and Statistical Metric Spaces, Kybernetika 11 (1975), 336–344. https://eudml.org/doc/28711.
- 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.
- S.U. Rehman, S. Jabeen, S.U. Khan, M.M.M. Jaradat, Some $alpha$-$phi$-Fuzzy Cone Contraction Results with Integral Type Application, J. Math. 2021 (2021), 1566348. https://doi.org/10.1155/2021/1566348.
- J.H. Park, Intuitionistic Fuzzy Metric Spaces, Chaos, Solitons Fractals 22 (2004), 1039–1046. https://doi.org/10.1016/j.chaos.2004.02.051.
- N. Konwar, Extension of Fixed Point Results in Intuitionistic Fuzzy b Metric Space, J. Intell. Fuzzy Syst. 39 (2020), 7831–7841. https://doi.org/10.3233/jifs-201233.
- M. Kirişci, N. Şimşek, Neutrosophic Metric Spaces, Math. Sci. 14 (2020), 241–248. https://doi.org/10.1007/s40096-020-00335-8.
- N. Simsek, M. Kirisci, Fixed Point Theorems in Neutrosophic Metric Spaces, Sigma J. Eng. Nat. Sci. 10 (2019), 221–230.
- S. Sowndrarajan, M. Jeyarama, F. Smarandache, Fixed point Results for Contraction Theorems in Neutrosophic Metric Spaces, Neutrosophic Sets Syst. 36 (2020), 308–318.
- 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.
- G.N.V. Kishore, R.P. Agarwal, B. Srinuvasa Rao, R.V.N. Srinivasa Rao, Caristi Type Cyclic Contraction and Common Fixed Point Theorems in Bipolar Metric Spaces with Applications, Fixed Point Theory Appl. 2018 (2018), 21. https://doi.org/10.1186/s13663-018-0646-z.
- B.S. Rao, G.N.V. Kishore, G.K. Kumar, Geraghty Type Contraction and Common Coupled Fixed Point Theorems in Bipolar Metric Spaces with Applications to Homotopy, Int. J. Math. Trends Technol. 63 (2018), 25–34. https://doi.org/10.14445/22315373/ijmtt-v63p504.
- G.N.V. Kishore, D.R. Prasad, B.S. Rao, V.S. Baghavan, Some Applications via Common Coupled Fixed Point Theorems in Bipolar Metric Spaces, J. Crit. Rev. 7 (2020), 601–607.
- G.N.V. Kishore, K.P.R. Rao, A. Sombabu, R.V.N.S. Rao, Related Results to Hybrid Pair of Mappings and Applications in Bipolar Metric Spaces, J. Math. 2019 (2019), 8485412. https://doi.org/10.1155/2019/8485412.
- U. Gürdal, A. Mutlu, K. Özkan, Fixed Point Results for $alpha$-$phi$-Contractive Mappings in Bipolar Metric Spaces, J. Inequal. Spec. Funct. 11 (2020), 64–75.
- A. Mutlu, K. Özkan, U. Gürdal, Locally and Weakly Contractive Principle in Bipolar Metric Spaces, TWMS J. Appl. Eng. Math. 10 (2020), 379–388.
- G.N.V. Kishore, K.P.R. Rao, H. IsIk, B. Srinuvasa Rao, A. Sombabu, Covarian Mappings and Coupled Fiexd Point Results in Bipolar Metric Spaces, Int. J. Nonlinear Anal. Appl. 12 (2021), 1–15. https://doi.org/10.22075/ijnaa.2021.4650.
- J.U. Maheswari, K. Dillibabu, G. Mani, S.T.M. Thabet, I. Kedim, et al., On New Common Fixed Point Theorems via Bipolar Fuzzy b-Metric Space with Their Applications, PLOS ONE 19 (2024), e0305316. https://doi.org/10.1371/journal.pone.0305316.
- G. Mani, A. Gnanaprakasam, P. Subbarayan, S. Chinnachamy, R. George, et al., Applications to Nonlinear Fractional Differential Equations via Common Fixed Point on $C^*$-Algebra-Valued Bipolar Metric Spaces, Fractal Fract. 7 (2023), 534. https://doi.org/10.3390/fractalfract7070534.
- G. Mani, A.J. Gnanaprakasam, S. Kumar, O. Ege, M. De la Sen, Fixed-Point Theorems for Nonlinear Contraction in Fuzzy-Controlled Bipolar Metric Spaces, Axioms 12 (2023), 396. https://doi.org/10.3390/axioms12040396.
- G. Mani, A.J. Gnanaprakasam, K. Javed, E. Ameer, S. Mansour, et al., On a Fuzzy Bipolar Metric Setting with a Triangular Property and an Application on Integral Equations, AIMS Math. 8 (2023), 12696–12707. https://doi.org/10.3934/math.2023639.
- G. Mani, A.J. Gnanaprakasam, H. Işık, F. Jarad, Fixed Point Results in $C^*$-Algebra-Valued Bipolar Metric Spaces with an Application, AIMS Math. 8 (2023), 7695–7713. https://doi.org/10.3934/math.2023386.
- G. Mani, R. Ramaswamy, A.J. Gnanaprakasam, V. Stojiljković, Z.M. Fadail, et al., Application of Fixed Point Results in the Setting of $F$-Contraction and Simulation Function in the Setting of Bipolar Metric Space, AIMS Math. 8 (2023), 10395–10396. https://doi.org/10.3934/math.2023526.
- Y.U. Gaba, M. Aphane, H. Aydi, $(alpha, BK)$-Contractions in Bipolar Metric Spaces, J. Math. 2021 (2021), 5562651. https://doi.org/10.1155/2021/5562651.
- S. Rawat, R.C. Dimri, A. Bartwal, $F$-Bipolar Metric Spaces and Fixed Point Theorems with Applications, J. Math. Comput. Sci. 26 (2021), 184–195. https://doi.org/10.22436/jmcs.026.02.08.
- L. Huang, X. Zhang, Cone Metric Spaces and Fixed Point Theorems of Contractive Mappings, J. Math. Anal. Appl. 332 (2007), 1468–1476. https://doi.org/10.1016/j.jmaa.2005.03.087.
- M. Gunaseelan, M. Narayan, M. Narayan, Fixed Point Theorems of Generalized Multi-Valued Mappings in Cone b-Metric Spaces, Math. Morav. 25 (2021), 31–45. https://doi.org/10.5937/matmor2101031g.
- D. Dey, M. Saha, Partial Cone Metric Space and Some Fixed Point Theorems, TWMS J. Appl. Eng. Math. 3 (2013), 1–9.
- T.L. Shateri, Common Fixed Point Results in Partial Cone Metric Spaces, arXiv:2208.06798 (2022). https://doi.org/10.48550/ARXIV.2208.06798.
- A. Arif, M. Nazam, A. Hussain, M. Abbas, The Ordered Implicit Relations and Related Fixed Point Problems in the Cone b-Metric Spaces, AIMS Math. 7 (2022), 5199–5219. https://doi.org/10.3934/math.2022290.
- A. Arif, M. Nazam, H.H. Al-Sulami, A. Hussain, H. Mahmood, Fixed Point and Homotopy Methods in Cone A-Metric Spaces and Application to the Existence of Solutions to Urysohn Integral Equation, Symmetry 14 (2022), 1328. https://doi.org/10.3390/sym14071328.