FIXED POINTS FOR FG(ξ; λ; θ)-GENERALIZED CONTRACTION WITH CG-CLASS FUNCTIONS IN bv(s)-METRIC SPACES
Abstract
The primary aim of this study is to establish the existence of a fixed point for FG(ξ, λ, θ)-generalized contractions in the context of bv(s)-metric spaces. The obtained result extends various well-established findings in metric spaces, b-metric spaces, rectangular b-metric spaces, and bv(s) metric spaces. Our discoveries not only expand upon and consolidate existing results in C-class functions but also build upon several previous contributions in the literature. Furthermore, we delve into and elaborate on the recently introduced concept of CG-class functions, providing illustrative examples.
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S. Aleksic, Z. D. Mitrovic and S. Radenovic: A fixed point theorem of Jungck in bv(s)-metric spaces. Period. Math. Hung. 77(2) (2018), 224-231.
A. H. Ansari: Note on φ − ψ contractive type mappings and related fixed point. The 2nd Regional Conference on Math. Appl. PNU (2014), 377-380.
A. H. Ansari and A. Kaewcharoen: C-class functions and fixed point theorems for generalized α-η-ψ-φ-F-contraction type mappings in α-η-complete metric spaces. Journal of Nonlinear Science and Applications, 9 (2016), 4177-4190.
S. Banach: Sur les operations dans les ensembles abstraits et leur application aux equations integrales. Fundam. Math. 3 (1922), 133-181.
J. Bogin: A generalization of a fixed point theorem of Goebel, Kirk and Shimi, Canadian Mathematical Bulletin. 19 (1976), 7-12.
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.
Lj. B. Ciric: Generalization of Banach’s contraction principle. Proceedings of the American Mathematical Society, 45(2) (1974), 267-273.
S. Czerwik: Contraction mappings in b-metric spaces. Acta Mathematica et Informatica Universitatis Ostraviensis. 1(1) (1993), 5-11.
F. Dong, P. Ji and X. Wang: Pata-Type Fixed Point Results in bv(s)-Metric Spaces. International Journal of Analysis and Applications, 17(3) (2019), 342-360.
T. Dosenovic, Z. Kadelburg, D. Mitrovic and S. Radenovic: New fixed point results in bv(s)-metric spaces. Mathematica Slovaca, 70(2) (2020), 441-452.
R. George, S. Radenovic, K. P. Reshma and S. Shukla: Rectangular b-metric space and contraction principles. J. Nonlinear Sci. Appl. 8(6) (2015), 1005-1013.
M. Edelstein: An extension of Banach’s contraction principle. Proceedings of the American Mathematical Society, 12 (1961), 7-10.
M. S. Khan, M. Swaleh and S. Sessa: Fixed point theorems by altering distances between the points. Bull. Austral Math. Soc. 30 (1984), 1-9.
B. K. Leta: Fixed Points for α − FG(ξ, λ, θ)-generalized Suzuki contraction with CG-class functions in bv(s)-metric spaces. TRENDS IN SCIENCES, 19(24), (2022).
Z. D. Mitrovic and S. Radenovic: The Banach and Reich contractions in bv(s)-metric spaces. J. Fixed Point Theory Appl. 19 (2017), 3087-3095.
O. Popescu: Two generalizations of some fixed point theorems. Comp. Math. Appl. 62(10) (2011), 3912-3919.
B. E. Rhoades: A Comparison of Various Definitions of Contractive Mappings.Transactions of the American Mathematical Society, 226 (1977), 257-290.
M. R. Taskovic: A Generalizations of Banach’s Contraction Principle. Publ. Inst. Math. 37(23) (1978), 179-191.
DOI: https://doi.org/10.22190/FUMI220110040K
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