Fixed point results of hybrid-type $F$-contractions

Subject Areas : Operator theory

M. S. Shagari ¹ , M. Jehoshaphat ² , R. O. Ogbumba ³ , R. Chiroma ⁴

1 - Department of Mathematics‎, ‎Faculty of Physical Sciences‎, ‎Ahmadu Bello University‎, ‎Zaria‎, ‎Nigeria
2 - Department of Mathematics‎, ‎Faculty of Physical Sciences‎, ‎Ahmadu Bello University‎, ‎Zaria‎, ‎Nigeria
3 - Department of Mathematics‎, ‎Faculty of Physical Sciences‎, ‎Ahmadu Bello University‎, ‎Zaria‎, ‎Nigeria
4 - Department of Mathematics‎, ‎Faculty of Physical Sciences‎, ‎Ahmadu Bello University‎, ‎Zaria‎, ‎Nigeria

Received: 2024-04-27 Accepted : 2024-08-30 Published : 2024-08-31

Keywords: Hybrid contraction, Jaggi-type contraction, $F$-contraction, fixed point,

Abstract :

‎This manuscript studies new concepts of hybrid $F$-contractions on a complete metric space‎. ‎It provides new conditions for the existence of fixed points for such mappings‎. ‎The main idea of this paper unifies a few important results in the corresponding literature‎. ‎Some of these consequences are highlighted and discussed as corollaries‎. ‎In support of the assumptions forming the theorems presented herein‎, ‎a comparative nontrivial example with a graphical illustration is provided‎.

References:

[1] R. P. Agarwal, U. Aksoy, E. Karapınar, I. M. Erhan, F-contraction mappings on metric-like spaces in connection with integral equations on time scales, RACSAM. 114 (2020), 3:147.

[2] M. Alansari, S. S. Mohammed, A. Azam, N. Hussain, On multivalued hybrid contractions with applications, Journal of Function Spaces. (2020), 1:5401403.

[3] H. Aydi, E. Karapınar, H. Yazidi, Modified F-contractions via α-admissible mappings and application to integral equations, Filomat. 31 (5) (2017), 1141-1148.

[4] S. Banach, Sur les oprations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3 (1) (1922), 133-181.

[5] B. K. Dass, S. Gupta, An extension of Banach contraction principle through rational expression, Indian J. Pure Appl. Math. 6 (12) (1975), 1455-1458.

[6] B. Hazarika, E. Karapınar, R. Arab, M. Rabbani, Metric-like spaces to prove existence of solution for nonlinear quadratic integral equation and numerical method to solve it, J. Comp. Appl. Math. 328 (2018), 302-313.

[7] D. S. Jaggi, Some unique fixed point theorems, Indian J. Pure Appl. Math. 8 (2) (1977), 223-230.

[8] J. A. Jiddah, M. Alansari, O. M. Mohamed, M. S. Shagari, A. A. Bakery, Fixed point results of Jaggi-type hybrid contraction in generalized metric space, Journal of Function Spaces. (2022), 1:2205423.

[9] E. Karapınar, Revisiting the Kannan-type contractions via interpolation, Adv. Theory. Nonl. Anal. Appl. 2 (2) (2018), 85-87.

[10] E. Karapınar, A. Fulga, A hybrid contraction that involves Jaggi type, Symmetry. 11 (2019), 5:715.

[11] E. Karapınar, A. Fulga, R. P. Agarwal, A survey: F-contractions with related fixed point results, J. Fixed Point Theory Appl. 22 (3) (2020), 1-58.

[12] E. Lotfali Ghasab, H. Majani, G. Soleimani Rad, Fixed points of set-valued F-contraction operators in quasi-ordered metric spaces with an application to integral equations, Journal of Siberian Federal University. Mathematics & Physics. 14 (2) (2021), 150-158.

[13] S. S. Mohammed, M. Alansari, A. Azam, S. Kanwal, Fixed points of (ϕ,F)-weak contractions on metric-like spaces with applications to integral equations on time scales, Bol. Soc. Mat. Mex. 27 (2021), 1-21.

[14] R. O. Ogbumba, M. S. Shagari, M. Alansari, T. A. Khalid, E. A. Mohamed, A. A. Bakery, Advancements in hybrid fixed point results and F-contractive pperators, Symmetry. 15 (2023), 6:1253.

[15] R. O. Ogbumba, M. S. Shagari, A. Azam, F. Ali, T. Alotaibi, Existence results of certain nonlinear polynomial and integral equations via z-contractive operators, AIMS Mathematics. 8 (12) (2023), 28646-28669.

[16] H. Piri, P. Kumam, Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory Appl. (2014), 2014:210.

[17] I. A. Rus, Generalized Contractions and Applications, Cluj University Press, Cluj-Napocca, Romania, 2001.

[18] N. A. Secelean, Iterated function systems consisting of F-contractions, Fixed Point Theory Appl. (2013), 2013:277.

[19] D. Singh, V. Chauhan, P. Kumam, V. Joshi, Some applications of fixed point results for generalized two classes of BoydWong’s F-contraction in partial b-metric spaces, Math. Sci. 12 (2) (2018), 111-127.

[20] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. (2012), 2020:94.

[21] D. Wardowski, Solving existence problems via F-contractions, Proc. Amer. Math. Soc. 146 (4) (2018), 1585-1598.

[22] D. Wardowski, N. Van Dung, Fixed points of F-weak contractions on complete metric spaces, Dem. Math. 47 (1) (2014), 146-155.

[23] S. Yahaya, M. S. Shagari, A. T. Imam, Fixed points of Ciric and Caristi-type multivalued contractions, J. Linear. Topological. Algebra. 12 (3) (2023), 201-209.