A New Fixed Point Result in Graphical $b_{v}(s)$-Metric Space with Application to Differential Equation
Download PDF
Authors: P. BARADOL, D. GOPAL AND N. DAMLJANOVIć
DOI: 10.46793/KgJMat2403.441B
Abstract:
In the present paper, motivated by [?, ?], first we give a notion of graphical bv(s)-metric space, which is a graphical version of bv(s)-metric space. Utilizing the graphical Banach contraction mapping we prove fixed point results in graphical bv(s)-metric space. Appropriate examples are also presented to support our results. In the end, the main result ensures the existence of a solution for an ordinary differential equation along with its boundary conditions by using the fixed point result in graphical bv(s)-metric space.
Keywords:
Graph, fixed point, graphical bv(s) metric, graphic Banach contraction.
References:
[1] S. Aleksić, H. Huang, Z. D. Mitrović and S. Radenović, Remarks on some fixed point results in b-metric spaces, J. Fixed Point Theory Appl. 20(4) (2018), Article ID 147, 17 pages. https://doi.org/10.1007/s11784-018-0626-2
[2] I. A. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal. Ulianowsk Gos. Ped. Inst. 30 (1989), 26–37.
[3] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3 (1922), 133–181.
[4] P. Baradol, D. Gopal and S. Radenović, Computational fixed points in graphical rectangular metric spaces with application, J. Comput. Appl. Math. 375 (2020), Article ID 112805, 12 pages. https://doi.org/10.1016/j.cam.2020.112805
[5] P. Baradol, J. Vujaković, D. Gopal and S. Radenović, On some new results in graphical rectangular b-metric spaces, Mathematics 8(4) (2020), Article ID 488, 17 pages. https://doi.org/10.3390/math8040488
[6] A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen 57(1–2) (2000), 31–37. http://dx.doi.org/10.12988/imf.2014.4227
[7] D. W. Boyd and J. S. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20(2) (1969), 458–464. https://doi.org/10.1090/S0002-9939-1969-0239559-9
[8] J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions, Trans. Amer. Math. Soc. 215 (1976), 241–251. https://doi.org/10.1090/S0002-9947-1976-0394329-4
[9] N. Chuensupantharat, P. Kumam, V. Chauhan, D. Singh and R. Menon, Graphic contraction mappings via graphical b-metric spaces with applications, Bull. Malays. Math. Sci. Soc. 42 (2019), 3149–3165. https://doi.org/10.1007/s40840-018-0651-8
[10] Lj. B. Ćirić, A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc. 45(2) (1974), 267–273. https://doi.org/10.2307/2040075
[11] S. Czerwik, Contraction mappings in b-metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis 1 (1993), 5–11.
[12] J. Jachymski, Equivalence of some contractivity properties over metrical structures, Proc. Amer. Math. Soc. 125(8) (1997), 2327–2335.
[13] Z. Mitrović and S. Radenović, The Banach and Reich contractions in bv(s)-metric spaces, J. Fixed Point Theory Appl. 19(4) (2017), 3087–3095. https://doi.org/10.1007/s11784-017-0469-2
[14] B. Samet, C. Vetro and P. Vetro, Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Anal. 75(4) (2012), 2154–2165. https://doi.org/10.1016/j.na.2011.10.014
[15] S. Shukla, S. Radenović and C. Vetro, Graphical metric space: a generalized setting in fixed point theory. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM 111(3) (2017), 641–655. https://doi.org/10.1007/s13398-016-0316-0
[16] S. Shukla, N. Mlaiki and H. Aydi, On (G,G′)-Prešić–Ćirić operators in graphical metric spaces, Mathematics 7(5) (2019), Article ID 445, 12 pages. https://doi.org/10.3390/math7050445
[17] M. Younis, D. Singh and A. Goyal, A novel approach of graphical rectangular b-metric spaces with an application to the vibrations of a vertical heavy hanging cable, J. Fixed Point Theory Appl. 21(1) (2019), Article ID 3317 pages, https://doi.org/10.1007/s11784-019-0673-3
Login:
