New results on discontinuity at fixed point

R. P. Pant, Nihal Özgür, Nihal Taş, Abhijit Pant, Mahesh C. Joshi

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


We obtain a Meir–Keeler type fixed-point theorem which gives a new solution to the Rhoades’ problem on the existence of contractive mappings that admit discontinuity at the fixed point. Meir–Keeler type solutions of the Rhoades’ problem have not been reported in literature before this. Presenting a new approach, we give another solution to this problem using the set of simulation functions. To emphasize the importance of our theoretical results, we obtain two applications of the main results with some illustrative examples.

Original languageEnglish
Article number39
JournalJournal of Fixed Point Theory and Applications
Issue number2
Publication statusPublished - 1 Jun 2020
Externally publishedYes


  • Fixed point
  • discontinuity
  • fixed circle
  • fixed disc
  • simulation function

ASJC Scopus subject areas

  • Modeling and Simulation
  • Geometry and Topology
  • Applied Mathematics


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