Mathematica Bohemica, Vol. 148, No. 2, pp. 223-236, 2023
Fixed point theorems for hybrid pair of weak compatible mappings
in partial metric spaces
Santosh Kumar, Johnson Allen Kessy
Received December 19, 2020. Published online June 6, 2022.
Abstract: The notions of compatible mappings play a crucial role in metrical fixed point theory. Partial metric spaces are a generalization of the notion of a metric space in the sense that distance of a point from itself is not necessarily zero. In this paper, we prove coincidence and fixed point theorems for a pair of single-valued and multi-valued weak compatible mappings on a complete partial metric space. Our main results generalize, in particular, the results of Kaneko and Sessa (1989), Pathak (1995) and Kessy, Kumar and Kakiko (2017). Examples that illustrate the generality of our results are also provided.
Affiliations: Santosh Kumar, Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam, 35065 Dar es Salaam, Tanzania, e-mail: email@example.com; Johnson Allen Kessy, Department of Mathematics, College of Natural and Mathematical Sciences, University of Dodoma, P.O. Box 259 Dodoma, Tanzania, e-mail: firstname.lastname@example.org