Common Fixed Points of Generalized Interpolative Kannan-Meir-Keeler Pair Contraction

Authors

  • Rohit Kumar Verma Department of Mathematics, Govt. Chandulal Chandrakar Arts and Science College, Patan, Durg 491001, Chhattisgarh, India https://orcid.org/0009-0002-1428-5505
  • Jaynendra Shrivas Department of Mathematics, Govt. V. Y. T. PG Autonomous College, Durg 491001, Chhattisgarh, India https://orcid.org/0009-0009-3470-8975
  • Prachi Singh Department of Mathematics, Govt. V. Y. T. PG Autonomous College, Durg 491001, Chhattisgarh, India https://orcid.org/0000-0002-3901-5811
  • Kuleshwari Department of Mathematics, Govt. V. Y. T. PG Autonomous College, Durg 491001, Chhattisgarh, India https://orcid.org/0009-0008-4582-718X

DOI:

https://doi.org/10.26713/jims.v17i3.3275

Abstract

In this paper, we introduce a generalized version of Meir-Keeler type contraction by incorporating interpolative conditions for a pair of mappings in metric spaces. We establish new common fixed point theorems that extend as well as unify several well-known results in the literature. Our findings generalize and enhance the recent results of Noorwali et al. [10].

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References

A. Alam and M. Imdad, Relation-theoretic contraction principle, Journal of Fixed Point Theory and Applications 17(4) (2015), 693 – 702, DOI: 10.1007/s11784-015-0247-y.

S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundamenta Mathematicae 3(1) (1922), 133 – 181, URL: https://eudml.org/doc/213289.

D. Gopal and R. K. Bisht, Metrical common fixed points and commuting type mappings, in Background and Recent Developments of Metric Fixed Point Theory, D. Gopal, P Kuman and M. Abbas, CRC Press, (2017).

G. Jungck, Commuting mappings and fixed points, The American Mathematical Monthly 83(4) (1976), 261 – 263, DOI: 10.2307/2318216.

R. Kannan, Some results on fixed points, Bulletin of the Calcutta Mathematical Society 60 (1968), 71 – 76.

R. Kannan, Some results on fixed points II, The American Mathematical Monthly 76(4) (1969), 405 – 408, DOI: 10.2307/2316437.

E. Karapınar, Revisiting the Kannan type contractions via interpolation, Advances in the Theory of Nonlinear Analysis and its Application 2(2) (2018), 85 – 87, DOI: 10.31197/atnaa.431135.

E. Karapınar, Interpolative Kannan-Meir-Keeler type contraction, Analysis and Its Application 5(4) (2021), 611 – 614, URL: https://atnaea.org/index.php/journal/article/view/228.

A. Meir and E. Keeler, A theorem on contraction mappings, Journal of Mathematical Analysis and Applications 28(2) (1969), 326 – 329, DOI: 10.1016/0022-247X(69)90031-6.

M. Noorwali, Common fixed point for Kannan type contractions via interpolation, Journal of Mathematical Analysis 9(6) (2018), 92 – 94, URL: http://www.ilirias.com/jma/repository/docs/JMA9-6-8.pdf.

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Published

2025-09-16
CITATION

How to Cite

Verma, R. K., Shrivas, J., Singh, P., & Kuleshwari. (2025). Common Fixed Points of Generalized Interpolative Kannan-Meir-Keeler Pair Contraction. Journal of Informatics and Mathematical Sciences, 17(3), 305–314. https://doi.org/10.26713/jims.v17i3.3275

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Research Article