International Journal of Nonlinear Analysis and Applications

Fixed point for $\alpha_{*}$-$\psi$-$\beta_{i}$-contractive set-valued mappings on Branciari $S_{b}$-metric space

Document Type : Research Paper

Authors

1 Department of Mathematics‎, ‎Faculty of Science‎, ‎Tabriz Branch‎, ‎Islamic Azad‎ ‎‎‎University‎, ‎Tabriz‎, ‎Iran

2 Department of Mathematics, Faculty of Science, Tabriz Branch, Islamic Azad University, Tabriz, Iran

3 Department of Mathematics, Semnan University, Semnan, Iran

Abstract

In 1984, Khan et al. established some fixed point theorems in complete and compact metric spaces by altering distance functions. In 2020, Lotfy et al. introduced the $\alpha_{*}$-$\psi$-common rational type mappings on generalized metric spaces applied to fractional integral equations. In 2022, Roy et al. described the notion of Branciari  $ S_b$-metric space and related fixed point theorems with an application. In this paper, we introduce the notion of fixed point theorems for $\alpha_{*}$-$\psi$-$\beta_{i}$-contractive set-valued mappings on Branciari $S_{b}$-metric space with application to fractional integral equations.

Keywords

[1] M. Abbas, T. Nazir, and S. Radenovic, Common fixed points of four maps in partially ordered metric spaces, Appl. Math. Lett. 24 (2011), 1520–1526.
[2] I. Altun and V. Rakocevic, Ordered cone metric spaces and fixed point results, Comput. Math. Appl. 60 (2010), no. 5, 1145–1151.
[3] M. Asadi, H. Soleimani, and S.M. Vaezpour, An order on subsets of cone metric spaces and fixed points of set-valued contractions, Fixed Point Theory Appl. 2009 (2009), Article ID 723203, 8 pages.
[4] A. Branclari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Pub. Math. Debrecen 57 (2000), no. 1-2, 31–37.
[5] B.C. Dhage, Condensing mappings and applications to existence theorems for common solution of differential equations, Bull. Korean Math. Soc. 36 (2000), no. 3, 565–578.
[6] B.C. Dhage, D. Oregan, and R.P. Agarwal, Common fixed theorems for a pair of countably condensing mappings in ordered Banach spaces, J. Apple. Math Stoch. Anal. 16 (2003), no. 3, 243–248.
[7] M. Eshaghi Gordji, M. Ramezani, M. De La Sen, and Y.J. Cho, On orthogonal sets and Banach fixed point theorem, Fixed Point Theory 18 (2017), no. 2, 569–578.
[8] A. Farajzadeh, A. Kaewcharoen, and P. Lahawech, On Fixed point theorems for (ξ,α,η)-Expansive mappings in complete metric spaces, Int. J. Pure Appl. Math. 102 (2015), no. 1, 129.
[9] Y. Feng and S. Liu, Fixed point theorems for multi-valued increasing operators in partially ordered spaces, Soochow J. Math. 30 (2004), no. 4, 461–469.
[10] D. Guo and V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications, Nonlinear Anal.: Theory Meth. Appl. 11 (1987), 623–632.
[11] J. Hassanzadeh Asl, Common fixed point theorems for α-ψ-contractive type mappings, Int. J. Anal. 2013 (2013), 1- -7.
[12] J. Hassanzadeh Asl, Sh. Rezapour, and N. Shahzad, On fixed points of α-ψ-contractive multifunctions, Fixed Point Theory Appl. 2012 (2012), 1–6.
[13] Z. Kadelburg and S. Radenovic, On generalized metric spaces, A survey, TWMS J. Pure Appl. Math. 5 (2014), 3—13.
[14] W.A. Kirk and N. Shahzad, Generalized metrics and Caristi's theorem, Fixed Point Theory Appl. 2013 (2013), Article ID 129.
[15] M.S. Khan, M. Swaleh, and S. Sessa, Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc. 30 (1984), no. 1, 1–9.
[16] F. Lotfy and J. Hassanzadeh Asl, Some fixed point theorems for α∗-ψ-common rational type mappings on generalized metric spaces with application to fractional integral equations, Int. J. Nonlinear Anal. Appl. 12 (2021), no. 1, 245–260.
[17] Y. Rohen, T. Dosenovic, and S. Radenovic, A fixed point theorems in Sb-metric spaces, Filomat 31 (2017), no. 11, 3335–3346.
[18] K. Royy and M. Saha, Branciari Sb-metric space and related fixed point theorems with an application, Appl. Math. E-Notes 22 (2022), 8–17.
[19] S. Sedghi and N.V. Dung, Fixed point theorems on S-metric spaces, Mat. Vesnik 66 (2014), 113—124.
[20] B. Samet, C. Vetro, and P. Vetro, Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Anal. 75 (2012), 2154–2165.
[21] S. Sedghi, N. Shobe, and A. Aliouche, A generalization of fixed point theorems in S-metric spaces, Mat. Vesnik 64 (2012), 258–266.
[22] N. Souayah and N. Mlaiki, A fixed point theorem in Sb-metric spaces, J. Math. Comput. Sci. 16 (2016), 131-–139.
International Journal of Nonlinear Analysis and Applications
Volume 15, Issue 12
December 2024
Pages 369-384
  • Receive Date: 11 August 2022
  • Revise Date: 15 January 2024
  • Accept Date: 01 February 2024