Multivalued relation-theoretic graph contraction principle with applications

Document Type : Research Paper


1 Department of Mathematics, Graphic Era Hill University, Uttarakhand, India

2 Government Degree college, Purwala Dogi, Uttarakhand, India

3 Department of Mathematics, HNB Garhwal University, Srinagar(Garhwal), Uttarakhand, India

4 Department of Mathematics, Graphic Era (Deemed to be) University, Dehradun, Uttarakhand, India

5 Department of Mathematics, HNB Garhwal University, Campus Pauri, Uttarakhand, India


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.


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Volume 13, Issue 2
July 2022
Pages 2961-2971
  • Receive Date: 02 February 2021
  • Revise Date: 11 June 2022
  • Accept Date: 24 July 2022