Interpolative Berinde Weak Mapping Theorem on Partial Metric Spaces

  • Clement Boateng Ampadu 31 Carrolton Road, Boston, MA 02132-6303, USA
Keywords: interpolative Berinde weak operator, partial metric spaces, fixed point theorem

Abstract

In this paper we introduce the notion of an interpolative Berinde weak operator in partial metric spaces. Additionally, we give an existence theorem for such operators in partial metric spaces. Finally, in support of the existence theorem, we provide an example.

References

Banach, S. (1922). Sur les operations dans les ensembles abstraits et leur applications aux equations integrales. Fundamenta Mathematicae, 3, 133–181. https://doi.org/10.4064/fm-3-1-133-181

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

Karapinar, E. (2018). Revisiting the Kannan type contractions via interpolation. Advances in the Theory of Nonlinear Analysis and Applications, 2, 85–87. https://doi.org/10.31197/atnaa.431135

Reich, S. (1971). Some remarks concerning contraction mappings. Canadian Mathematical Bulletin, 14, 121–124. https://doi.org/10.4153/CMB-1971-024-9

Reich, S. (1972). Fixed point of contractive functions. Bollettino dell'Unione Matematica Italiana, 4, 26–42.

Reich, S. (1971). Kannan's fixed point theorem. Bollettino dell'Unione Matematica Italiana, 4, 1–11.

Rus, I. A. (1979). Principles and applications of the fixed point theory. Editura Dacia, Cluj-Napoca, Romania. (In Romanian)

Rus, I. A. (2001). Generalized contractions and applications. Cluj University Press, Cluj-Napoca, Romania.

Matthews, S. G. (1994). Partial metric topology. Annals of the New York Academy of Sciences, 728, 183–197. https://doi.org/10.1111/j.1749-6632.1994.tb44144.x

Karapinar, E., Agarwal, R., & Aydi, H. (2018). Interpolative Reich-Rus-Ciric type contractions on partial metric spaces. Mathematics, 6(256). https://doi.org/10.3390/math6110256

Altun, I., Sola, F., & Simsek, H. (2010). Generalized contractions on partial metric spaces. Topology and Its Applications, 157, 2778–2785. https://doi.org/10.1016/j.topol.2010.08.017

Aydi, H., Karapinar, E., & Kumam, P. (2013). A note on "Modified proof of Caristi's fixed point theorem on partial metric spaces". Journal of Inequalities and Applications, 2013, 355. https://doi.org/10.1186/1029-242X-2013-355

Aydi, H., Amor, S. H., & Karapinar, E. (2013). Berinde type generalized contractions on partial metric spaces. Abstract and Applied Analysis, 2013, 312479. https://doi.org/10.1155/2013/312479

Aydi, H., Karapinar, E., & Shatanawi, W. (2011). Coupled fixed point results for (psi, phi)-weakly contractive condition in ordered partial metric spaces. Computers and Mathematics with Applications, 62, 4449–4460. https://doi.org/10.1016/j.camwa.2011.10.021

Aydi, H., Karapinar, E., & Rezapour, S. (2012). A generalized Meir-Keeler contraction type on partial metric spaces. Abstract and Applied Analysis, 2012, 287127. https://doi.org/10.1155/2012/287127

Aydi, H., & Karapinar, E. (2012). A Meir-Keeler common type fixed point theorem on partial metric spaces. Fixed Point Theory and Applications, 2012, 26. https://doi.org/10.1186/1687-1812-2012-26

Ciric, L. J., Samet, B., Aydi, H., & Vetro, C. (2011). Common fixed points of generalized contractions on partial metric spaces and an application. Applied Mathematics and Computation, 218, 2398–2406. https://doi.org/10.1016/j.amc.2011.07.005

Chi, K. P., Karapinar, E., & Thanh, T. D. (2012). A generalized contraction principle in partial metric spaces. Mathematical and Computer Modelling, 55, 1673–1681. https://doi.org/10.1016/j.mcm.2011.11.005

Karapinar, E., Erhan, Y. M., & Ulus, A. Y. (2012). Fixed point theorem for cyclic maps on partial metric spaces. Applied Mathematics and Information Sciences, 6, 239–244.

Karapinar, E., Chi, K. P., & Thanh, T. D. (2012). A generalization of Ciric quasicontractions. Abstract and Applied Analysis, 2012. https://doi.org/10.1155/2012/518734

Ampadu, C. B. (2020). Some fixed point theory results for the interpolative Berinde weak operator. Earthline Journal of Mathematical Sciences, 4(2), 253–271. https://doi.org/10.34198/ejms.4220.253271

Published
2025-04-11
How to Cite
Ampadu, C. B. (2025). Interpolative Berinde Weak Mapping Theorem on Partial Metric Spaces. Earthline Journal of Mathematical Sciences, 15(4), 489-494. https://doi.org/10.34198/ejms.15425.489494
Section
Articles

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