Some fixed point theorems for $\alpha_{*}$-$\psi$-common rational type mappings on generalized metric‎ spaces with application to fractional integral equations

Document Type : Research Paper


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


‎‎Recently Hamed H Alsulami et al introduced the notion of‎ ‎($\alpha$-$\psi$)-rational type contractive mappings‎. ‎They have been‎ ‎establish some fixed point theorems for the mappings in complete‎ ‎generalized metric spaces‎. ‎In this paper‎, ‎we introduce the notion‎ ‎of some fixed points theorems for $\alpha_{*}$-$\psi$-common‎ ‎rational type mappings on generalized metric spaces with application‎ ‎to fractional integral equations and give a common fixed point‎ ‎result about fixed points of the‎ ‎set-valued mappings‎.


[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] H.H. Alsulami, S. Chandok, M.A. Taoudi and I.M. Erhan, Some common fixed points theorems for α∗-ψ-common rational type contractive and weakly increasing multi-valued mappings on ordered metric spaces, Fixed Point Theory Appl. 2015 (2015) 97.
[3] I. Altun and V. Rakocevic, Ordered cone metric spaces and fixed point results, CAMWA-D-09 00221, (2009).
[4] A. Amini-Harandi, Coupled and tripled fixed point theory in partially ordered metric spaces with application to initial value problem, Math. Comput. Model. 2012 (2012) doi:10.1016/j.mcm.2011.12.006.
[5] 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.
[6] M. Asadi, E. Karapinar and A. Kumar, α-ψ-Geraghty contractions on generalized metric spaces, J. Inequal. Appl. 2014 (2014).
[7] M. Asadi, E. Karapinar and P. Salimi, A new approach to G-metric and related fixed point theorems, J. Inequal. Appl. 2013 (2013) 454.
[8] H. Baghani, M. E. Gordji and M. Ramezani, Orthogonal sets: The axiom of choice and proof of a fixed point theorem, J. Fixed Point Theory Appl. 18(3) (2016) 465–477.
[9] A. Branclari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces Publ. Math (Debe) 57 (2000) 31–37.
[10] 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(3) (2003) 243–248.
[11] M.E. Gordji and H Habibi, Fixed point theory in generalized orthogonal metric space, J. Linear Topolog. Alg. 6(3(2017) 251–260.
[12] M.E. Gordji, M. Rameani, M. De La Sen and Y. Je Cho, On orthogonal sets and Banach fixed point theorem, Fixed Point Theory 18(2) (2017) 569–578.
[13] J. Hasanzadeh Asl, Sh. Rezapour and N. Shahzad, On fixed points of α-ψ-contractive multi-functions, Fixed Point Theory Appl. 2012 (2012) 212.
[14] J. Hasanzadehasl, Common fixed point theorems for α-ψ-contractive type mappings, Int. J. Anal. 2013 (2013), Article ID 654659.
[15] M. Ramezani and H. Baghani, Contractive gauge functions in strongly orthogonal metric spaces, Int. J. Nonlinear Anal. Appl. 8(2) (2017) 23–28.
[16] S. Khalehoghli, H. Rahimi and M. Eshaghi, Fixed point theorems in R-metric spaces with applications, AIMS Math. 5(4) (2020) 3125–3137.
[17] S. Khalehoghli, H. Rahimi and M. Eshaghi Gordji, R-topological spaces and SR-topological spaces with their applications, Math. Sci. 14(3) (2020) 249–255.
[18] B. Samet, C. Vetro and P. Vetro, Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Anal. 75 (2012) 2154–2165.
[19] W.A. Kirk and N. Shahzad, Generalized metrics and Caristi’s theorem, Fixed Point Theory Appl. 2013 (2013) Article ID 129.
[20] B.C. Dhage, Condensing mappings and applications to existence theorems for common solution of differential equations, Bull. Korean Math. Soc. 36(3) (1999) 565–578.
[21] D. Guo and V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications, Nonlinear Anal. Theory Meth. Appl. 11 (1987) 623–632.
[22] Y. Feng and S. Liu, Fixed point theorems for multi-valued increasing operators in partially ordered spaces, Soochow J. Math. 30(4) (2004) 461–469.
[23] W.A. Wilson, On semimetric spaces. Amer. J. Math. 53(2) (1931) 361–373.
Volume 12, Issue 1
May 2021
Pages 245-260
  • Receive Date: 04 April 2020
  • Revise Date: 12 November 2020
  • Accept Date: 02 January 2021