Fixed point theorems of Kannan-Pata hybrid operators in metric space and its few aspects

Author(s)	Dr. Animesh Upadhyay, Dr. Nikhilesh Metiya, Mr. Sunirmal Kundu, S. Dutta, S. P. Mondal
Country	India
Abstract	In this paper we define hybrid contraction by combining Kannan and Pata typecontraction. Where the former type is different from Banach contraction and admitsof possible discontinuities and the latter is a recent generalization of Banach contrac-tion. The main findings are fixed point results obtained for these hybrid contractionunder three different additional conditions. They are proved in an M -complete metricspace by an relation theoratic approach in which relation is additionally assumed in ametric space. Illustrative example is given. Uniqueness of the fixed point is established 2separately. Also well posedness property, error estimation and Ulam-Hyer’s stabilityof the fixed point problem are discussed in three different sections. An application toa problem of integral equation is also done. The research in the domain of relationtheoratic metric fixed point theory and its application.
Keywords	Metric space, binary relation, well posedness, error estimation, Ulam-Hyer’s stability, integral equation.
Field	Mathematics
Published In	Volume 7, Issue 4, July-August 2025
Published On	2025-08-23
DOI	https://doi.org/10.36948/ijfmr.2025.v07i04.53265
Short DOI	https://doi.org/g9x22x

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