Affiliation:
1. Department of Mathematics , Aligarh Muslim University , Aligarh , India
Abstract
Abstract
In this article, we discuss the relation theoretic aspects of multivalued weakly contractive mappings to prove fixed point results in the setting of metric spaces endowed with a certain binary relation.
Our newly proved results generalize, extend, unify, enrich, sharpen and improve some well-known fixed point theorems of existing literature to the case of multivalued and contractive notion.
We also incorporated an example and an application to find the solution of a Volterra-type integral inclusion.
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics, Probability and Uncertainty,Mathematical Physics
Reference31 articles.
1. A. Alam, M. Arif and M. Imdad,
Metrical fixed point theorems via locally finitely 𝑇-transitive binary relations under certain control functions,
Miskolc Math. Notes 20 (2019), no. 1, 59–73.
2. A. Alam and M. Imdad,
Relation-theoretic contraction principle,
J. Fixed Point Theory Appl. 17 (2015), no. 4, 693–702.
3. A. Alam and M. Imdad,
Relation-theoretic metrical coincidence theorems,
Filomat 31 (2017), no. 14, 4421–4439.
4. A. Alam, F. Sk and Q. H. Khan,
Discussion on generalized nonlinear contractions,
Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 84 (2022), no. 2, 23–34.
5. Y. I. Alber and S. Guerre-Delabriere,
Principle of weakly contractive maps in Hilbert spaces,
New Results in Operator Theory and its Applications,
Oper. Theory Adv. Appl. 98,
Birkhäuser, Basel (1997), 7–22.