Expanded Rectangular b-Metric Spaces and Fixed Point Results for Nonlinear F-Contractions
Keywords:
fixed point, expanded rectangular b-metric space, F-contraction, nonlinear F-contractionAbstract
The generalization of metric space is one of research directions that focus on fixed point theory. Recently, many generalizations of metric spaces have been introduced and the related fixed point results in these abstract spaces have been established. In this paper, we introduce a new concept called expanded rectangular b-metric space by combining the ideas of expanded b-metric space and rectangular metric space. We claim that expanded rectangular b-metric space is another generalization of metric space, b-metric space, expanded b-metric space, rectangular metric space, and rectangular b-metric space, and we give examples to illustrate this. We also prove fixed point result of nonlinear F-contractions under weaker assumptions in such metric spaces. Our fixed point results generalize and improve many of the previous well-known fixed point results. Finally, we apply obtained result to consider the existence of solutions for nonlinear integral equation.
Downloads
References
[1] M. Abbas, R. Anjum and H. Iqbal, Generalized enriched cyclic contractions with application to generalized iterated function system, Chaos, Solitons & Fractals, 154 (2022), 111591. 1
[2] T. Abdeljawad, N. Mlaiki, H. Aydi and N. Souayah, Double controlled metric type spaces and some fixed point results, Mathematics, 6 (2018), 320. 1
[3] M. Asim, M. Imdad and S. Radenovi´c, Fixed point results in extended rectangular b-metric spaces with an application, U.P.B. Sci. Bull., Series A, 20 (2019), 43–50. 1, 2.3
[4] I.A. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal., Gos. Ped. Inst., Unianowsk, 30 (1989), 26-37. 1
[5] A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math., 57 (2000), 31–37. 1, 2.1
[6] M. Dhanzeem Ahmed and D. Easwaramoorthy, Fractal attractor via controlled strong b-Kannan iterated function system, International Journal of Analysis and Applications, 23 (2025), 155. 1
[7] R. George, S. Radenovi´c, K. P. Reshma and S. Shukla, Rectangular b-metric space and contraction principles, J. Nonlinear Sci. Appl., 8 (2015), 1005–1013. 1, 2, 2.2, 3.12
[8] T. Kamran, M. Samreen and Q. Ul Ain, A generalization of b-metric space and some fixed point theorems, Mathematics, 5 (2017), 19. 1
[9] A. Karami, S. Sedghi, Z. D. Mitrovic, Solving existence problems via contractions in expanded b-metric spaces, The Journal of Analysis, 30 (2022), 895–907. 1, 2, 2.5
[10] E. Karapinar, S. Sedghi and N. Shobe, Solving existence problems via F-contraction in modified b-metric spaces, TWMS J. App. and Eng. Math., 12 (2022), 1526-1535. 1, 4
[11] N. Mlaiki, H. Aydi, N. Souayah and T. Abdeljawad, Controlled metric type spaces and the related contraction principle, Mathematics, 6 (2018), 194. 1
[12] Z. Mustafa, V. Parvaneh, M.M.M. Jaradat and Z. Kadelburg, Extended Rectangular b-Metric Spaces and Some Fixed Point Theorems for Contractive Mappings, Symmetry, 11 (2019), 594. 1, 2.4
[13] T. Nazir and A. Zakaria Idriss, Iterated function systems of generalized multivalued mappings in partial metric spaces, Contemporary Mathematics, 6(5) (2025), 5368-5387. 1
[14] V. Parvaneh and S.J.H. Ghoncheh, Fixed points of (Ψ,Φ)Ω-contractive mappings in ordered p-metric spaces, Global Analysis and Discrete Mathematics, 4 (2020), 15–29. 1
[15] N.A. Secelean, Iterated function system consisting of F-contractions, Fixed Point Theory Appl., 2013 (2013), 277. 2
[16] Z. S. Tasneem, K. Gopalan and T. Abdeljawad, A different approach to fixed point theorems on triple controlled metric type spaces with a numerical experiment, Dynamic Systems and Applications, 30 (2021), 111–130. 1
[17] Z. S. Tasneem, K. Gopalana and T. Abdeljawad, Controlled b-Branciari Metric Type Spaces and Related Fixed Point Theorems with Applications, Filomat, 34 (2020), 4253–4269. 1
[18] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory and Appl., 2012 (2012), 94. 2.6, 2.7
[19] D. Wardowski, Solving existence problems via F-contractions, Proceedings of the American Mathematical Society, 146 (2018), 1585–1598. 2, 2.8
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Chol Jin Kil, Un-A Ri, Song-Gyong Ri, Un-Hye Ku
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
