TARU PUBLICATIONS
Journal of Interdisciplinary Mathematics cover
Hybrid ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

On the extreme points of the sets

*

* Corresponding author · click or hover a name for details

pp. 1–7Online FirstApril 2026DOI: 10.47974/JIM-2388XML
Received:
01 Apr 2025
Published Online:
01 Apr 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2388
Pages:
1–7

Abstract

In this paper, extreme points of the convex sets are considered. Some properties of the extreme points are stated and proved. 

Keywords

Subject Classifications

90C49

References

[1] C. D. Aliprantis and K. C. Border, Infinite Dimensional Analysis: A Hitchhiker’s Guide, 3rd ed., Springer, Berlin–Heidelberg–New York (2006). 
[2] V. G. Boltyanski, H. Martini, and P. Soltan, Excursions into Combinatorial Geometry, Springer, Berlin–Heidelberg–New York (1997). 
[3] S. Boyd, L. Vandenberghe, Convex Optimization, Cambridge University Press, Cambridge (2004). 
[4] C. J. Goh, X. Q. Yang, Duality in Optimization and Variational Inequalities, Taylor & Francis, London–New York (2002). 
[5] B. Grünbaum, Convex Polytopes, 2nd ed., Springer, New York–Berlin–Heidelberg (2003). 
[6] L. Narici and E. Beckenstein, Topological Vector Spaces, 2nd ed., Chapman and Hall / CRC Press, Boca Raton (2010). 
[7] A. G. Ramm, P. N. Shivakumar, and A. V. Strauss (eds.), Operator Theory and Its Applications, American Mathematical Society, Providence (2000). 
[8] R. T. Rochafellar, Convex Analysis, Princeton Unoversity Press, Princeton (1970). 
[9] H. H. Schaefer and M. P. Wolff, Topological Vector Spaces, 2nd ed., Springer, New York (1999). 
[10] V. Soltan, “Support and separation properties of convex sets in finite dimension”, Extracta Mathematicae, vol. 36, no. 2, pp. 241-278 (2021). 
[11] S. M. Stefanov, “Valid inequalities and cutting planes for some polytopes”, Mathematical Inequalities and Applications, vol. 1, no. 2, pp. 285-294 (1998). 
[12] S. M. Stefanov, Convex Separable Programming, Kluwer Academic Publishers, Dordrecht (2000). 
[13] S. M. Stefanov, Separable Programming: Theory and Methods, Kluwer Academic Publishers, Dordrech–Boston–London (2001). 
[14] S. M. Stefanov, “Valid inequalities, cutting planes and integrality of the knapsack polytope”, Journal of Interdisciplinary Mathematics, vol. 14, no. 4, pp. 389-406 (2011). 
[15] S. M. Stefanov, “On the solution of quadratic programming problem with a feasible region defined as a Minkowski sum of a compact set and finitely generated convex closed cone”, Journal of Information and Optimization Sciences, vol. 39, no. 6, pp. 1223-1230 (2018). 
[16] S. M. Stefanov, Separable Optimization: Theory and Methods, Springer, Cham (2021). 
[17] S. M. Stefanov, “Continuous linear knapsack problems revisited”, Journal of Information and Optimization Sciences, vol. 44, no. 5, pp. 909-922 (2023). 
[18] S. M. Stefanov, “On the separation of sets”, Journal of Interdisciplinary Mathematics, published online. 
[19] S. M. Stefanov, “Supporting hyperplanes and separation of sets”, Journal of Interdisciplinary Mathematics, to appear.

Views: 99Downloads: 117Citations: 0