Fixed Point Theorems for Hybrid Contractions in Partial Metric Spaces

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Published: 2022-10-12

Page: 657-665


Preeti Bhardwaj

Department of Mathematics, Baba Mastnath University, Asthal Bohar, Rohtak, Haryana, India.

Manoj Kumar *

Department of Mathematics, Baba Mastnath University, Asthal Bohar, Rohtak, Haryana, India.

*Author to whom correspondence should be addressed.


Abstract

In this paper, we shall introduce the hybrid contraction of type A and type B and prove fixed point theorems for such contractions in partial metric spaces.

Keywords: Partial metric space, fixed point theorem, hybrid contraction


How to Cite

Bhardwaj, Preeti, and Manoj Kumar. 2022. “Fixed Point Theorems for Hybrid Contractions in Partial Metric Spaces”. Asian Journal of Pure and Applied Mathematics 4 (1):657-65. https://www.jofmath.com/index.php/AJPAM/article/view/56.

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References

Ćirić L. A generalization of Banach’s contraction principle. Proc. Am. Math. Soc. 1974;45:267–273.

Kannan R. Some results on fixed points. Bull. Calcutta Math. Soc. 1968;60:71–76.

Reich S. Some remarks concerning contraction mappings. Can. Math. Bull. 1971;14:121–124.

Rus IA. Generalized contractions and applications. Cluj University Press: Clui-Napoca, Romania; 2001.

Mustafa Z, Sims B. A new approach to a generalized metric space. Journal of Nonlinear Convex Analysis. 2006;7(2):289-297.

Zeqing L, Wang Li, Shin M, Kang, Kim Y. Fixed point theorems in metric spaces. International Journal of Pure and Applied Mathematics. 2007;38:225-232.

Matthews SG. Partial metric topology. Proceedings of the 8th Summer Conferenceon Topology and its Applications, Annals of the New York Academy of Sciences. 1994;728:183–197.

Alqahtani B, Aydi H, Karapınar E, Rakočević V. A solution for volterra fractional integral equations by hybrid contractions. Mathematics. 2019;7(8):694.

Matthews SG. Partial metric topology, Research report 2012, Deptartment of Com-puter Science, University of Warwick; 1992.

Karapinar E. Revisiting the Kannan type contractions via interpolation. Adv. Theory Nonlinear Anal. Appl. 2018;2:85–87.

Agarwal RP, Karapinar E. Interpolative rus-reich-ciric type contractions via simulation functions. Analele Stiintifice ale Universitatii Ovidius Constanta Seria Matematica; 2019, in press.

Aydi H, Karapinar E, de Hierro AFRL. ω-Interpolative ciric-reich-rus-type contractions. Mathematics. 2019;7:57.

Aydi H, Chen CM, Karapinar E. Interpolative Ciric-Reich-Rus type contractions via the Branciari distance. Mathematics. 2019;7:84.

Karapinar E, Alqahtani O, Aydi H. On interpolative Hardy-Rogers type contractions. Symmetry. 2019;11:8.