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mmr 2021, 7(1): 67-82 |
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Ranjbar S, Khatibzadeh H, Ahmadi P. Convexity and Geodesic Metric Spaces. mmr 2021; 7 (1) :67-82
URL: http://mmr.khu.ac.ir/article-1-2930-en.html
URL: http://mmr.khu.ac.ir/article-1-2930-en.html
1- Higher Education Center of Eghlid , sranjbar@eghlid.ac.ir
2- University of Zanjan
2- University of Zanjan
Abstract: (1893 Views)
In this paper, we first present a preliminary study on metric segments and geodesics in metric spaces. Then we recall the concept of d-convexity of sets and functions in the sense of Menger and study some properties of d-convex sets and d-convex functions as well as extreme points and faces of d-convex sets in normed spaces. Finally we study the continuity of d-convex functions in geodesic metric spaces.
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Keywords: Geodesic, Metric segment, d-convex set, Metric convex hull, d-convex function, Extreme point, Continuity.
Type of Study: Original Manuscript |
Subject:
Anal
Received: 2019/03/17 | Revised: 2021/05/24 | Accepted: 2019/11/9 | Published: 2021/05/31 | ePublished: 2021/05/31
Received: 2019/03/17 | Revised: 2021/05/24 | Accepted: 2019/11/9 | Published: 2021/05/31 | ePublished: 2021/05/31
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