On n-ellipse contractive mappings over some extended metric spaces

• Roy, Kushal ^[3] ; Mitrovic, Zoran D. ^[1] ; Parvaneh, Vahid ^[2]
  1. [1] University of Banja Luka

     University of Banja Luka

     Bosnia y Herzegovina

     
  2. [2] Islamic Azad University, Arak

     Islamic Azad University, Arak

     Irán

     
  3. [3] Dr. B. C. Roy Engineering College

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• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 26, Nº. 2, 2025, págs. 799-813
• Idioma: inglés
• DOI: 10.4995/agt.2025.23158
• Enlaces
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• Resumen

  • In this paper, the concept of a mapping contracting axes of an n-ellipse is introduced and its fixed point set has been determined. Investigation of fixed point of mappings over different metric-type spaces is always an interesting study in fixed point theory. We consider a mapping with special characteristic, which is contracting axes of an n-ellipse over two different metric-type structures, Δ -metric space and ℱ -metric space. An enriched version of a mapping contracting axes of an n-ellipse is also introduced, and this class of mappings includes several non-expansive mappings. Moreover, the paper is furnished by some suitable examples that support our results and show that our mapping is distinct from the usual contractive type mappings.

• Referencias bibliográficas
  • I. A. Bakhtin, Contracting mapping principle in an almost metric space, (Russian), Funkts. Anal. 30 (1989), 26-37. https://doi.org/10.1039/ap9892600037
  • 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
  • V. Berinde and M. Păcurar, Approximating fixed points of enriched contractions in Banach spaces, J. Fixed Point Theory Appl. 22 (2020), 38....
  • V. Berinde and M. Păcurar, Kannan's fixed point approximation for solving split feasibility and variational inequality problems, J. Comput....
  • V. Berinde and M. Păcurar, Approximating fixed points of enriched Chatterjea contractions by Krasnoselskij iterative algorithm in Banach spaces,...
  • S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav. 1 (1993), 5-11.
  • M. Jleli and B. Samet, On a new generalization of metric spaces, J. Fixed Point Theory Appl. 20, no. 3 (2018), 128. https://doi.org/10.1007/s11784-018-0606-6
  • M. Joshi, A. Tomar, and S. K. Padaliya, Fixed point to fixed ellipse in metric spaces and discontinuous activation function, Appl. Math. E-Notes...
  • T. Kamran, M. Samreen, and Q. U. Ain, A generalization of b-metric space and some fixed point theorems, Mathematics 5 (2017), 19. https://doi.org/10.3390/math5020019
  • N. Y. Ozgur and N. Tas, 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. Ozgur and N. Tas, Some fixed-circle theorems and discontinuity at fixed circle, AIP Conf. Proc. 1926 (2018), 020048. https://doi.org/10.1063/1.5020497
  • S. Panja, K. Roy, and M. Saha, Wardowski type enriched contractive mappings with their fixed points, J. Anal. 32 (2024), 169-281. https://doi.org/10.1007/s41478-023-00626-y
  • R. P. Pant, Discontinuity and fixed points, J. Math. Anal. Appl. 240 (1999), 284-289. https://doi.org/10.1006/jmaa.1999.6560
  • V. Parvaneh and S. J. H. Ghoncheh, Fixed points of (ψ,φ)_Ω-contractive mappings in ordered p-metric spaces, Glob. Anal. Discret. Math. 4,...
  • E. Petrov, Fixed point theorem for mappings contracting perimeters of triangles, arXiv:2308.01003v1.
  • B. E. Rhoades, Contractive definitions and continuity, Contemp. Math. 72 (1988), 233-245. https://doi.org/10.1090/conm/072/956495
  • K. Roy, Mappings contracting axes of ellipse, J. Anal. 32 (2024), 3557-3563. https://doi.org/10.1007/s41478-024-00819-z
  • K. Roy, D. Dey, and M. Saha, Certain fixed point results on U-metric space using Banach orbital contraction and asymptotic regularity, Math....
  • K. Roy and M. Saha, Fixed point theorems for a class of extended JS-contraction mappings over a generalized metric space with an application...
  • K. Roy, M. Saha, V. Parvaneh, and M. Khorshidi, A new variant of symmetric distance spaces and an extension of the Banach fixed point theorem,...
  • N. Tas, H. Aytimur, and S. Guvencc, New fixed figure results with the notion of k-ellipse, arXiv:2112.10204v1.