Multivalued fixed point theorem involving hybrid contraction of the Jaggi-Suzuki Type
Main Article Content
Abstract
In this manuscript, a new multi-valued contraction is defined from a combination of Jaggi-type hybrid contraction and Suzuku-type hybrid contraction. Conditions for the existence of fixed points for such contractions in metric space are investigated. Moreover, some consequences are highlighted and discussed to indicate the significance of our proposed ideas. An example is given to support the assumptions of our theorems.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License.
References
[1] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. math. 3 (1) (1922), 133–181. Google Scholar
[2] S. B. Nadler, Multi-valued contraction mappings, Paci. J. Math. 30 (2) (1969), 475–488. Google Scholar
[3] L. B. Ciric, A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc. 45 (2) (1974), 267–273. Google Scholar
[4] B. K. Dass and S. Gupta, An extension of Banach contraction principle through rational expression, Indian J. Pure Appl. Math. 6 (12) (1975), 1455–1458. Google Scholar
[5] D. S. Jaggi, Some unique fixed point theorems, Indian J. Pure Appl. Math. 8 (2) (1977), 223–230. Google Scholar
[6] T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (5) (2008), 1861–1869. Google Scholar
[7] O. Popescu, Some new fixed point theorems for α-Geraghty contraction type maps in metric spaces, Fixed Point Theo. Appl. (1) (2014). Google Scholar
[8] E. Karapinar, Revisiting the Kannan type contractions via interpolation, Adv. Theo. Nonl. Anal. Appl. 2 (2) (2018), 85–87. Google Scholar
[9] M. Noorwali, Common fixed point for Kannan type contractions via interpolation, J. Math. Anal. 9 (6) (2018), 92–94. Google Scholar
[10] O. Alqahtani and E. Karapınar, A bilateral contraction via simulation function, Fil. 33 (15) (2019), 4837–4843. Google Scholar
[11] C.-M. Chen, G. H. Joonaghany, E. Karapınar and F. Khojasteh, On Bilateral Contractions, Math. 7 (6) (2019). https://dx.doi.org/10.3390/math7060538 Google Scholar
[12] E. Karapınar, K. Farshid and S. Wasfi, Revisiting Cırıc-Type Contraction with Caristi’s Approach, Symm. 11 (2019). https://dx.doi.org/10.3390/sym11060726 Google Scholar
[13] E. Karapinar and A. Fulga, A hybrid contraction that involves Jaggi type, Symm. 11 (5) (2019). Google Scholar
[14] S. B. Nadler, Multi-valued contraction mappings, Pacific J. Math. 30 (2) (1969), 475–488. Google Scholar
[15] M. S. Shagari, I. A. Fulatan and S. Yahaya, Common fixed points of L-Fuzzy maps for Meir-Keeler type contractions, J. Adv. Math. Stud. 12 (2) (2019), 218–229. Google Scholar
[16] A. Zikria, M. Samreen, T. Kamran and V. Yesilkaya, Periodic and fixed points for Caristi-type G-contractions in extended b-gauge spaces, J. Func. Spaces (2021), Article ID 1865172. Google Scholar
[17] E. Karapinar, S. M. De La and A. Fulga, A note on the Gornicki-Proinov type contraction, J. Func. Spaces (2021), Article ID 6686644. Google Scholar
[18] M. S. Shagari, U. I. Foluke, S. Yahaya and I. A. Fulatan, New Multi-valued Contractions with Applications in Dynamic Programming, Inter. J. Math. Scie. and Opti.: Theory and Appl. 6 (2) (2021), 924–938. Google Scholar
[19] Z. D. Mitrovic, H. Aydi, M. S. M. Noorani and H. Qawaqneh, The weight inequalities on Reich type theorem in b-metric spaces, J. Math. and Comp. Scie. 19 (1) (2019), 51–57. Google Scholar
[20] K. Abodayeh, E. Karapınar, A. Pitea and W. Shatanawi, Hybrid Contractions on Branciari Type Distance Spaces, Math. 7 (10) (2019). https://dx.doi.org/10.3390/math7100994 Google Scholar
[21] N. Maha and S. Y. Seher, On Jaggi-Suzuki type hybrid contraction mappings, J. Func. Spaces (2021). https://dx.doi.org/10.1155/2021/6721296 Google Scholar
[22] M. S. Shagari, S. Yahaya and I. A. Fulatan, On Fixed Point results in F-metric space with applications to neutral differential equations, Math. Anal. Contemp. Appl. 4 (3) (2022), 47–62. Google Scholar