Common Fixed Points of Generalized Interpolative Kannan-Meir-Keeler Pair Contraction
DOI:
https://doi.org/10.26713/jims.v17i3.3275Abstract
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].
Downloads
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.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.



