Investigation of a fixed point problem for Pata-type contractions with respect to w-distance

Pata-type mappings satisfy an uncountably infinite set of inequalities parameterized by an index varying over a closed interval. Fixed point problems involving these mappings have been of considerable interest in recent times. The use of w -distance has made possible several generalizations of fixed...

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Bibliographic Details
Published in:The Journal of Analysis Vol. 32; no. 1; pp. 125 - 136
Main Authors: Roy, Subhadip, Chakraborty, Priyam, Ghosh, Sumon, Saha, Parbati, Choudhury, Binayak S.
Format: Journal Article
Language:English
Published: Singapore Springer Nature Singapore 01.02.2024
Springer Nature B.V
Subjects:
Abstract Harmonic Analysis
Analysis
Fourier Analysis
Functional Analysis
Investigations
Mathematics
Mathematics and Statistics
Measure and Integration
Original Research Paper
Special Functions
47H10
Metric space
distance
47H09
Integral equation
Pata-type contraction
Fixed point
Well-posedness
54H25
ISSN:0971-3611, 2367-2501
Online Access:Get full text
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Summary:Pata-type mappings satisfy an uncountably infinite set of inequalities parameterized by an index varying over a closed interval. Fixed point problems involving these mappings have been of considerable interest in recent times. The use of w -distance has made possible several generalizations of fixed point results in metric fixed point theory. Combining the above two contemporary trends of research, we investigate a fixed point problem pertaining to Pata-type mappings by using w -distance. We establish a new existence and uniqueness fixed point result. We cite examples to show that the new result is a proper generalization of the corresponding result in metric spaces and that the theorem applies to some discontinuous functions as well. The problem of well-posedness formulated with respect to w -distance is also investigated. Finally, the fixed point problem obtained herein is applied to integral equations.
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ISSN:0971-3611
2367-2501
DOI:10.1007/s41478-023-00612-4