Journal of Fixed Point Theory and Applications

, Volume 17, Issue 4, pp 693–702 | Cite as

Relation-theoretic contraction principle

  • Aftab Alam
  • Mohammad ImdadEmail author


In this paper, we present yet another new and novel variant of classical Banach contraction principle on a complete metric space endowed with a binary relation which, under universal relation, reduces to Banach contraction principle. In process, we observe that various kinds of binary relations, such as partial order, preorder, transitive relation, tolerance, strict order, symmetric closure, etc., utilized by earlier authors in several well-known metrical fixed point theorems can be weakened to the extent of an arbitrary binary relation.


Complete metric spaces binary relations contraction mappings 

Mathematics Subject Classification

47H10 54H25 


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of MathematicsAligarh Muslim UniversityAligarhIndia

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