The Journal of Analysis

, Volume 26, Issue 1, pp 151–162 | Cite as

Fixed point theorems for weakly contractive mappings in relational metric spaces with an application

  • Gopi Prasad
  • Ramesh Chandra Dimri
Original Research Paper


In this paper, we prove fixed point theorem for weakly contractive mappings using locally T-transitivity of binary relation and presenting a variant of Harjani and Sadarangani theorem involving more general relation theoretic metrical notions. Our results under universal relation reduces to Harjani and Sadarangani (Nonlinear Anal 71:3403–3410, 2009) fixed point theorems. We also generalize some recent fixed point theorems for weak contraction such as Alam and Imdad (J Fixed Point Theory Appl 17(4):693–702, 2015) and Kutbi et al. (Fixed Point Theory Appl 2015:198, 2015) besides some others.


\(\mathcal {R}\)-continuity Locally T-transitive binary relation Weakly contractive map 

Mathematics Subject Classification

47H10 54H25 



The authors thank the referees for their careful reading of the manuscript and insightful comments.

Author contributions

All authors contributed equally to the writing of this paper. All authors read and approved the final manuscript.

Compliance with ethical standards

Conflict of interest

All the authors declare that there is no conflict of interests.


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Copyright information

© Forum D'Analystes, Chennai 2018

Authors and Affiliations

  1. 1.Department of MathematicsH.N.B. Garhwal UniversityGarhwalIndia

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