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Multivalued relation-theoretic graph contraction principle with applications | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 237، دوره 13، شماره 2، مهر 2022، صفحه 2961-2971 اصل مقاله (400.37 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.22536.2381 | ||
| نویسندگان | ||
| Deepak Khantwal* 1؛ Surbhi Aneja2؛ Gopi Prasad3؛ B. C. Joshi4؛ U.C. Gairola5 | ||
| 1Department of Mathematics, Graphic Era Hill University, Uttarakhand, India | ||
| 2Government Degree college, Purwala Dogi, Uttarakhand, India | ||
| 3Department of Mathematics, HNB Garhwal University, Srinagar(Garhwal), Uttarakhand, India | ||
| 4Department of Mathematics, Graphic Era (Deemed to be) University, Dehradun, Uttarakhand, India | ||
| 5Department of Mathematics, HNB Garhwal University, Campus Pauri, Uttarakhand, India | ||
| تاریخ دریافت: 14 بهمن 1399، تاریخ بازنگری: 21 خرداد 1401، تاریخ پذیرش: 02 مرداد 1401 | ||
| چکیده | ||
| In this paper, we present a new generalization of Nadler's fixed point theorem for multivalued relation-theoretic graph contractions on relational metric spaces. Our results extend and generalize the result of Shukla and Rodriguez-Lopez (Questiones Mathematiae, (2019) 1-16), Nadler (Pacific J. Math. 30 (1969), 475-488), Alam and Imdad (J. Fixed Point Theory and Appl., 17(4) (2015), 693-702) and many others in the existing literature of fixed point theory. Some illustrative examples are also provided to illustrate the usefulness of our main results. Moreover, we have an application to generalized coupled fixed point problems. | ||
| کلیدواژه‌ها | ||
| fixed point؛ coupled fixed point؛ contraction mapping؛ binary relation | ||
| مراجع | ||
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[1] A. Alam and M. Imdad , Relation-theoretic contraction principle, J. Fixed Point Theory Appl. 17 (2015), 693–702. [2] A. Alam and M. Imdad, Nonlinear contractions in metric spaces under locally T-transitive binary relations, Fixed Point Theory 19 (2018), 13–23. [3] H. Baghani and M. Ramezani, A fixed point theorem for a new class of set-valued mappings in R-complete (not necessarily complete) metric spaces, Filomat 31 (2017), 3875–3884. [4] S. Banach, Sur les op´erations dans les ensembles abstraits et leur application aux ´equations int´egrales, Fund. Math. 3 (1922), 133–181. [5] H. Ben-El-Mechaiekh , The Ran-Reurings fixed point theorem without partial order: a simple proof, J. Fixed Point Theory Appl. 16 (2014), 373–383. [6] D. Khantwal, S. Aneja, G. Prasad and U.C. Gairola , A generalization of relation-theoretic contraction principle, TWMS J. App. Eng. Math. (Accepted). [7] S.B. Nadler Jr, Multivalued contraction mappings, Pacific J. Math. 30 (1969), 475–488. [8] J.J. Nieto and R. Rodr´ıguez-L´opez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005), 223–239. [9] A. Petru¸sel, G. Petru¸sel and J. Yao, Multi-valued graph contraction principle with applications, Optim. 69 (2020), 1541–1556. [10] G. Prasad and R. C. Dimri, Fixed point theorems for weakly contractive mappings in relational metric spaces with an application, J. Anal. 26 (2018), 151–162. [11] A.C.M. Ran and M.C.B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004), 1435–1443. [12] B. Samet and M. Turinici, Fixed point theorems on a metric space endowed with an arbitrary binary relation and applications, Commun. Math. Anal. 13 (2012), 82–97. [13] S. Shukla and R. Rodr´ıguez-L´opez, Fixed points of multi-valued relation-theoretic contractions in metric spaces and application, Q. Math. 43 (2020), 409–424. [14] A. Tomar, M. Joshi, S.K. Padaliya, B. Joshi and A. Diwedi, Fixed point under set-valued relation-theoretic nonlinear contractions and application, Filomat 33 (2019), 4655–4664. [15] M. Turinici, Nieto-Lopez theorems in ordered metric spaces, Math. Stud. 81 (2012), 219–229. | ||
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