Warianty tytułu
Języki publikacji
Abstrakty
In this article, fixed point results for self-mappings in the setting of two metrics satisfying F -lipschitzian conditions of rational-type are proved, where F is considered as a semi-Wardowski function with constant τ∈R instead of τ>0 . Two metrics have been considered, one as an incomplete while the other is orbitally complete. The mapping is taken to be orbitally continuous from one metric to another. Some examples are provided to validate our results. For applications, we present existence results for the solutions of a new type of ABC-fractional boundary value problem.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
452--469
Opis fizyczny
Bibliogr. 28 poz.
Twórcy
autor
- International Islamic University, H-10, Islamabad, Pakistan , nayyarmaths@gmail.com
autor
- Department of Mathematics, Namal University, Mianwali, 30 Km Talagang Rd, Mianwali 42250, Pakistan, israr.khan@namal.edu.pk
autor
- Islamabad Model College for Boys I-8/3, Islamabad, Pakistan, ayyazmaths@yahoo.com
autor
- International Islamic University, H-10, Islamabad, Pakistan , niaz.ahmad@iiu.edu.pk
Bibliografia
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- [3] S. K. Chatterjea, Fixed-point theorems, Dokl. Bolg. Akad. Nauk. 25 (1972), no. 6, 727–730.
- [4] G. J. De Cabral-Garciiiiia, K. Baquero-Mariaca, and J. Villa-Morales, A fixed point theorem in the space of integrable functions and applications, Rend. Circ. Mat. Palermo 2 (2022), 1–18, DOI: https://doi.org/10.1007/s12215-021-00714-7.
- [5] R. Kannan, Some results on fixed points, Bull. Cal. Math. Soc. 60 (1968), 71–76.
- [6] E. Karapinar, A short survey on the recent fixed point results on b-metric spaces, Constr. Math. Anal. 1 (2018), no. 1, 15–44.
- [7] M. A. Khamsi and W. A. Kirk, An Introduction to Metric Spaces and Fixed Point Theory, John Wiley and Sons, 2011.
- [8] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012 (2012), 94.
- [9] M. G. Maia, Un’osservazione sulle contrazioni metriche, Math. J. Univ. Padova 40 (1968), 139–143.
- [10] B. Fisher, Mappings satisfying a rational inequality, Bull. Math. Soc. Sci. Math. Répub. Social. Roum. 24 (1980), no. 3, 247–251.
- [11] M. S. Khan, A fixed point theorem for metric spaces, Rend. Ist. Mat. Univ. Trieste 8 (1976), 69–72.
- [12] E. Karapinar, A. Fulga, and R. P. Agarwal, A survey: F-contractions with related fixed point results, J. Fixed Point Theory Appl. 22 (2020), no. 3, 1–58.
- [13] M. Olgun, T. Alyıldız, Ö. Biçer, and I. Altun, Fixed point results for F-contractions on space with two metrics, Filomat 31 (2017), no. 17, 5421–5426.
- [14] D. Wardowski, Solving existence problems via F -contractions, Proc. Amer. Math. Soc. 146 (2018), no. 4, 1585–1598.
- [15] I. A. Rus, On a fixed point theorem in a set with two metrics, Anal. Numér. Théor. Approx. 6 (1977), no. 2, 197–201.
- [16] J. T. Machado, V. Kiryakova, and F. Mainardi, Recent history of fractional calculus, Commun. Nonlinear Sci. Numer. Simul. 16 (2011), no. 3, 1140–1153.
- [17] S. Abbas, M. Benchohra, and J. J. Nieto, Caputo-Fabrizio fractional differential equations with non instantaneous impulses, Rend. Circ. Mat. Palermo (2) 71 (2022), no. 1, 131–144.
- [18] J. Zhou, Y. Deng, and Y. Wang, Variational approach to p-Laplacian fractional differential equations with instantaneous and non-instantaneous impulses, Appl. Math. Lett. 104 (2020), 106251.
- [19] Y. Zhao, C. Luo, and H. Chen, Existence results for noninstantaneous impulsive nonlinear fractional differential equation via variational methods, Bull. Malays. Math. Sci. Soc. 43 (2020), no. 3, 2151–2169.
- [20] I. A. Rus, On a fixed point theorem of Maia, Studia Univ. Babes-Bolyai Math. 22 (1977), 40–42.
- [21] G. Mınak, A. Helvacı, and I. Altun, Ćirić type generalized F-contractions on complete metric spaces and fixed point results, Filomat 28 (2014), no. 6, 1143–1151.
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- [24] K. Goebel and B. Sims, Mean Lipschitzian mappings, Contemp. Math. 513 (2010), 157–167.
- [25] M. Turinici, Wardowski Implicit Contractions in Metric Spaces, 2013, arXiv: http://arXiv.org/abs/arXiv:1211.3164.
- [26] T. Abdeljawad and D. Baleanu, Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel, J. Nonlinear Sci. Appl. 10 (2017), 1098–1107.
- [27] A. Atangana and D. Baleanu, New fractional derivatives with nonlocal and non-singular kernel theory and application to heat transfer model, Therm. Sci. 20 (2016), no. 2, 763–769.
- [28] T. Abdeljawad, A Lyapunov type inequality for fractional operators with nonsingular Mittag-Leffler kernel, J. Inequal. Appl. 2017 (2017), 130.
Uwagi
PL
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
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