New contractions in modular metric spaces and applications
Main Article Content
Abstract
This article discusses new contraction mappings with reference to modular metric spaces. It examines conditions for such operators to have invariant points. A nontrivial case is shown to illustrate the veracity of the established results. From applications point of consideration, it is observed that the ideas proposed herein allow for the presentation of a general criteria for solving a class of integral equations.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License.
References
[1] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3 (1) (1922), 133–181. Google Scholar
[2] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 60 (1968), 71–76. Google Scholar
[3] M. S. Shagari, R. Chiroma, T. Alotaibi, M. Noorwali, A. Saliu, and A. Azam, Notes on quasi contractive operators and their applications, Res. Math. 11 (1) (2024), 2424598. https://doi.org/10.1080/27684830.2024.2424598 Google Scholar
[4] S. Yahaya, M. S. Shagari, and I. A. Fulatan, Fixed points of bilateral multivalued contractions, Filomat 38 (8) (2024), 2835–2846. Google Scholar
[5] H. Nakano, Modulared Semi-Ordered Linear Spaces, Tokyo Math. Book Ser., Vol. 1, Maruzen Co., Tokyo (1950). Google Scholar
[6] S. Koshi and T. Shimogaki, On F-norms of quasi-modular spaces, J. Fac. Sci. Hokkaido Univ. Ser. I 15 (3-4) (1961), 202–218. Google Scholar
[7] S. Yamamuro, On conjugate spaces of Nakano spaces, Trans. Amer. Math. Soc. 90 (1959), 291–311. Google Scholar
[8] V. V. Chistyakov, Modular metric spaces I: Basic concepts, Nonlinear Anal. 72 (1) (2010), 1–14. https://doi.org/10.1016/j.na.2009.04.057 Google Scholar
[9] V. V. Chistyakov, Modular metric spaces II: Application to superposition operators, Nonlinear Anal. 72 (1) (2010), 15–30. https://doi.org/10.1016/j.na.2009.04.018 Google Scholar
[10] C. Mongkolkeha, W. Sintunavarat, and P. Kumam, Fixed point theorems for contraction mappings in modular metric spaces, Fixed Point Theory Appl. 2011 (2011), Article ID 93. https://doi.org/10.1186/1687-1812-2011-93 Google Scholar
[11] S. Kumar, L. D. Sharma, A. Chanda, and Z. D. Mitrović, On some non-linear contractions in modular metric spaces, Filomat 34 (12) (2020), 3971–3980. Google Scholar
[12] M. Younis, D. Singh, S. Radenović, and M. Illati, Convergence theorems for generalized contractions and applications, Filomat 34 (3) (2020), 945–964. Google Scholar
[13] Y. Sharma and S. Jain, Coupled fixed point theorems in modular metric spaces endowed with a graph, Kyungpook Math. J. 61 (2) (2021), 441–453. https://doi.org/10.5666/KMJ.2021.61.2.441 Google Scholar
[14] F. S. Al-shammari, R. K. P., R. Rajagopalan, and R. George, Generalised Presic type operators in modular metric space and an application to integral equations of Carathéodory type functions, J. Math. 2021 (2021), Article ID 7915448, 20 pages. https://doi.org/10.1155/2021/7915448 Google Scholar
[15] D. Das, S. Nandi, Y. M. Singh, M. S. Khan, and S. Sessa, Fixed point results on partial modular metric space, Axioms 11 (2) (2022), Article ID 62. https://doi.org/10.3390/axioms11020062 Google Scholar
[16] H. H. Alsulami, S. Chandok, M. A. Taoudi, and I. M. Erhan, Some fixed point theorems for (α,ψ)-rational type contractive mappings, Fixed Point Theory Appl. 2015 (2015), Article ID 97. https://doi.org/10.1186/s13663-015-0332-3 Google Scholar
[17] S. G. Talebi, A. Bodaghi, and A. N. Motlagh, Some results in metric modular spaces, Int. J. Nonlinear Anal. Appl. 13 (2) (2022), 983–988. https://doi.org/10.22075/ijnaa.2022.25676.3091 Google Scholar
[18] H. Rahimpoor, Some contraction fixed point theorems in partially ordered modular metric spaces, Int. J. Nonlinear Anal. Appl. 14 (9) (2023), 273–282. https://doi.org/10.22075/ijnaa.2021.25264.2971 Google Scholar
[19] H. Rahimpoor and I. Nikoufar, Some results for cyclic weak contractions in modular metric space, J. Linear Topol. Algebra 12 (1) (2023), 57–66. Google Scholar
[20] G. A. Okeke and D. Francis, Some common fixed point theorems in generalized modular metric spaces with applications, Sci. Afr. 23 (2024), e02018. https://doi.org/10.1016/j.sciaf.2023.e02018 Google Scholar
[21] D. Păcurar and A. Păcurar, Convex contractive mappings in generalized metric spaces, U.P.B. Sci. Bull. Ser. A 86 (2) (2024), 21–30. Google Scholar
[22] W. A. J. Luxemburg, Banach Function Spaces, Ph.D. Thesis, Delft University of Technology, Assen, The Netherlands (1955). Google Scholar
[23] J. Musielak and W. Orlicz, On modular spaces, Studia Math. 18 (1) (1959), 49–65. Google Scholar
[24] J. Musielak and W. Orlicz, Some remarks on modular spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 7 (1959), 661–668. Google Scholar
[25] M. Berinde, Approximate fixed point theorems, Stud. Univ. Babeş-Bolyai Math. 51 (1) (2006), 11–25. Google Scholar
[26] E. Karapınar and A. Fulga, An admissible hybrid contraction with an Ulam type stability, Demonstr. Math. 52 (1) (2019), 428–436. https://doi.org/10.1515/dema-2019-0037 Google Scholar
[27] X. Z. Wu and L. Hao, Fixed point theorems for generalized α-ψ type contractive mappings in b-metric spaces and applications, J. Math. Comput. Sci. 18 (1) (2018), 49–62. https://doi.org/10.22436/jmcs.018.01.06 Google Scholar