O‘zbekiston matematika jurnali Volume 70 Issue 2 (2026) · pp. 208-217

Geometric and topological properties of the Minkowski operator on convex sets

Zaitov, Adilbek, Nuritdinov, Jalolxon

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Abstract

This paper systematically establishes the fundamental geometrical and topological properties of the Minkowski operator on convex sets in an Euclidean space. The convexity, closedness, and boundary properties of the Minkowski sum and difference are analyzed. In addition, results concerning the Minkowski sum and difference of open and closed sets are presented. The paper also constructs illustrative examples to clarify each of the obtained results.

Convex setsMinkowski differenceMinkowski sumhomothetic setboundary of a setcompact set

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Cite

APA 7 
Zaitov, Adilbek & Nuritdinov, Jalolxon (2026). Geometric and topological properties of the Minkowski operator on convex sets. O‘zbekiston matematika jurnali, 70(2), 208-217.
GOST R 7.0.5 
Zaitov, Adilbek, Nuritdinov, Jalolxon Geometric and topological properties of the Minkowski operator on convex sets // O‘zbekiston matematika jurnali. 2026. Т. 70. № 2. С. 208-217.
BibTeX 
@article{adilbek2026,
  author  = {Zaitov, Adilbek and Nuritdinov, Jalolxon},
  title   = {Geometric and topological properties of the Minkowski operator on convex sets},
  journal = {O‘zbekiston matematika jurnali},
  year    = {2026},
  volume  = {70},
  number  = {2},
  pages   = {208-217}
}
RIS 
TY  - JOUR
AU  - Zaitov, Adilbek
AU  - Nuritdinov, Jalolxon
TI  - Geometric and topological properties of the Minkowski operator on convex sets
JO  - O‘zbekiston matematika jurnali
PY  - 2026
VL  - 70
IS  - 2
SP  - 208
EP  - 217
ER  -