Mappings contracting transverse axis of hyperbola
Submitted: 2025-03-27
|Accepted: 2026-01-08
|Published: 2026-03-16
Copyright (c) 2025 Kushal Roy
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Downloads
Keywords:
Fixed point, hyperbola, mappings contracting transverse axis of hyperbola, complete metric space
Supporting agencies:
Abstract:
In this paper a new contractive type mapping known as mapping contracting transverse axis of hyperbola is introduced. This mapping can reduce the length of transverse axis of a hyperbola. This is a geometric technique that is connected to the study of geometric characteristics of certain curves defined over metric spaces. The paper is decorated by some suitable examples that support our proven results and showing the distinctness of our mapping from the usual contractive type mappings. Our proposed mapping also admits discontinuity at fixed point, thus gives a new solution to an open problem posed by B.E. Rhoades. Finally a geometric figure is illustrated to describe the speciality of our mapping.
References:
S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations untegrales, Fund. Math. 3 (1922), 133-181.https://doi.org/10.4064/fm-3-1-133-181
R. K. Bisht, An overview of the emergence of weaker continuity notions, various classes of contractive mappings and related fixed point theorems, J. Fixed Point Theory Appl. 25 (2023), 11.
https://doi.org/10.1007/s11784-022-01022-y
Lj. B. Ćirić, On contraction type mappings, Math. Balkanica 1 (1971), 52-57.
M. Joshi, A. Tomar and S. K. Padaliya, Fixed point to fixed ellipse in metric spaces and discontinuous activation function, Applied Mathematics E-Notes 21 (2021), 225-237.
N. Y. Özgür and N. Taş, N. Some fixed-circle theorems on metric spaces, Bull. Malays. Math. Sci. Soc.}, {42} (2019), 1433-1449. https://doi.org/10.1007/s40840-017-0555-z
N. Y. Özgür and N. Taş, Some fixed-circle theorems and discontinuity at fixed circle, AIP Conference Proceedings 1926, no. 1 (2018), 020048. https://doi.org/10.1063/1.5020497
A. Pant and R. P. Pant, Fixed points and continuity of contractive maps, Filomat 31, no. 11 (2017), 3501-3506.https://doi.org/10.2298/FIL1711501P
A. Pant, R. P. Pant, and M. C. Joshi, Caristi type and Meir-Keeler type fixed point theorems, Filomat 33, no. 12 (2019), 3711-3721.https://doi.org/10.2298/FIL1912711P
E. Petrov, Fixed point theorem for mappings contracting perimeters of triangles, J. Fixed Point Theory Appl. 25 (2023), 74.https://doi.org/10.1007/s11784-023-01078-4
K. Roy and M. Saha, Fixed point theorems for a class of extended $JS$-contraction mappings over a generalized metric space with an application to fixed circle problem, Proyecciones Journal of Mathematics, 41, no. 6 (2022), 1551-1572.https://doi.org/10.22199/issn.0717-6279-4363
K. Roy, Mappings contracting axes of ellipse, The Journal of Analysis 32 (2024), 3557-3563.https://doi.org/10.1007/s41478-024-00819-z
R. P. Pant, Discontinuity and fixed points, J. Math. Anal. Appl. 240 (1999), 284-289.https://doi.org/10.1006/jmaa.1999.6560
R. P. Pant, N. Y. Özgür, and N. Taş, On discontinuity problem at fixed point, Bull. Malays. Math. Sci. Soc. 43, no. 1 (2020), 499-517.https://doi.org/10.1007/s40840-018-0698-6
B. E. Rhoades, Contractive definitions and continuity, Contemporary Mathematics 72 (1988), 233-245.https://doi.org/10.1090/conm/072/956495
