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Peer-reviewedCC BY 4.0Mathematics

Structural Properties of Isosymmetric Transformations on Metric Spaces

  • Sid Ahmed Ould Ahmed Mahmoud1
  • Ali Hamzah Alibrahim1
  1. 1Mathematics Department, College of Science, Jouf University, P.O. Box 2014, Sakaka 72388, Saudi Arabia
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Abstract

In this paper, we introduce and study m,n;q-isosymmetric transformations on metric spaces, generalizing the notions of m;q-isometries and n;q-symmetries that have recently been investigated in the literature. Our approach combines these two metric structures within a common framework governed by the parameters m, n, and q>0. We establish a collection of structural properties for m,n;q-isosymmetric transformations, including their behavior under iteration and composition, and derive several characterizations and equivalent conditions. We further examine their relationships with Lipschitz, nonexpansive, and contractive mappings, revealing conditions under which the corresponding metric properties are inherited or recovered. In particular, we show how the new class connects the previously studied m;q-isometric and n;q-symmetric settings within a single metric framework. These results provide a foundation for the systematic study of the structure and behavior of isosymmetric transformations on metric spaces.

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Cite

BibTeXRIS
BibTeX
@article{mahmoud2026structural,
  title = {{Structural Properties of Isosymmetric Transformations on Metric Spaces}},
  author = {Sid Ahmed Ould Ahmed Mahmoud and Ali Hamzah Alibrahim},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14203726},
  url = {https://www.mdpi.com/2227-7390/14/20/3726},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Structural Properties of Isosymmetric Transformations on Metric Spaces
AU  - Sid Ahmed Ould Ahmed Mahmoud
AU  - Ali Hamzah Alibrahim
PY  - 2026
DA  - 2026/10/14
JO  - Mathematics
DO  - 10.3390/math14203726
UR  - https://www.mdpi.com/2227-7390/14/20/3726
AB  - In this paper, we introduce and study m,n;q-isosymmetric transformations on metric spaces, generalizing the notions of m;q-isometries and n;q-symmetries that have recently been investigated in the literature. Our approach combines these two metric structures within a common framework governed by the parameters m, n, and q>0. We establish a collection of structural properties for m,n;q-isosymmetric transformations, including their behavior under iteration and composition, and derive several characterizations and equivalent conditions. We further examine their relationships with Lipschitz, nonexpansive, and contractive mappings, revealing conditions under which the corresponding metric properties are inherited or recovered. In particular, we show how the new class connects the previously studied m;q-isometric and n;q-symmetric settings within a single metric framework. These results provide a foundation for the systematic study of the structure and behavior of isosymmetric transformations on metric spaces.
SN  - 2227-7390
ER  -