Volume 26 • Issue 1 • PP: 171-180 • 2025
Some results on fixed point in generalized metric spaces via an auxiliary function
View PDF Abstract
In this manuscript, we elegantly delineate the concept of JSφ-contractions within the realm of JS-metric spaces, as articulated by Jleli and Samet. Utilizing these contractions, we have formulated a groundbreaking fixed point theorem that paves the way for a diverse array of fixed point results. Additionally, we demonstrate a fixed point result specifically for P-contractions in JS-metric spaces. To further enrich our discourse, we provide several examples that vividly illustrate the essence of our principal theorem.
Keywords
References
[1] Banach, S.(1922). Sur les op´erations dans les ensembles abstraits et leur application aux ´equations int´egrales. fund. math, 3, 133-181.
[2] M. U. Ali, T. Kamran, M. Postolache, Fixed point theorems for multivalued G-contractions in Hausdorff b-Gauge spaces, J. Nonlinear Sci. Appl, 8(5) (2015), 847–855.
[3] A. Bejenaru, M. Postolache, On Suzuki mappings in modular spaces, Symmetry, 11(3) (2019), 319, https://doi.org/10.3390/sym11030319.
[4] S. Chandok, M. Postolache, Fixed point theorem for weakly Chatterjea-type cyclic contractions, Fixed Point Theory Appl., 2013 8 (2013), https://doi.org/10.1186/1687-1812-2013-28.
[5] Aydi, H., Karapinar, E., & Postolache, M. (2012). Tripled coincidence point theorems for weak Φ-contractions in partially ordered metric spaces, Fixed Point Theory Appl. 2012 44, https://doi.org/10.1186/1687-1812-2012-44.
[6] Batiha, I.M., Ouannas, A., Albadarneh, R., Al-Nana, A.A. and Momani, S. (2022), ”Existence and uniqueness of solutions for generalized Sturm–Liouville and Langevin equations via Caputo– Hadamard fractional-order operator”, Engineering Computations, Vol. 39 No. 7, pp. 2581-2603. https://doi.org/10.1108/EC-07-2021-0393
[7] Waseem G. Alshanti, Iqbal M. Batiha, Ma’mon Abu Hammad, Roshdi Khalil. (2023) A novel analytical approach for solving partial differential equations via a tensor product theory of Banach spaces, Partial Differential Equations in Applied Mathematics, Vol. 8, pages. 100531. https://doi.org/10.1016/j.padiff.2023.100531
[8] Ahmed Bouchenak, Iqbal M. Batiha, Mazin Aljazzazi, Iqbal H. Jebril, Mohammed Al-Horani, Roshdi Khalil, (2024), Atomic exact solution for some fractional partial differential equations in Banach spaces, Partial Differential Equations in Applied Mathematics, Vol. 9,pages 100626.
[9] Bakhtin, I.A.. (1989). The contraction mapping principle in almost metric spaces. funct. Anal., Gos. Ped. Inst., Unianowsk, 1989, 30, 26–37.
[10] S. Czerwik, Contraction mappings in b-metric spaces, Acta mathematica et informatica universitatis ostraviensis, 1(1) (1993), 5-11.
[11] Jleli, M., & Samet, B. (2014). A new generalization of the Banach contraction principle, Journal of inequalities and applications, 2014 38, https://doi.org/10.1186/1029-242X-2014-38.
[12] Dumitrescu, D. and Pitea, A., 2023. Fixed point theorems for (α, ψ)-rational type contractions in Jleli- Samet generalized metric spaces. AIMS Mathematics, 8(7), pp.16599-16617.
[13] Dumitrescu, D. and Pitea, A., 2022. Fixed Point Theorems on Almost (φ, θ)-Contractions in Jleli-Samet Generalized Metric Spaces. Mathematics, 10(22), p.4239.
Cite This Article
Choose your preferred format