تحدب در فضاهای متریک و ژئودزیک

نویسندگان
1 مرکز آموزش عالی اقلید، گروه ریاضیات و کاربردها
2 دانشگاه زنجان، گروه ریاضی
چکیده
در این مقاله، ابتدا بررسی مقدماتی روی پاره­خط­های متریک و ژئودزیک­ها در فضاهای متریک داریم. سپس با بازگو کردن تعریف تحدب متریک برای مجموعه­ها و توابع به بررسی برخی از ویژگی­های آنها به‌ویژه نقاط انتهایی و وجوه مجموعه‌های محدب متریک در فضاهای نرم­دار می­پردازیم. نهایتاً پیوستگی توابع محدب متریک را در فضاهای ژئودزیک بررسی می­کنیم.



کلیدواژه‌ها

عنوان مقاله English

Convexity and Geodesic Metric Spaces

نویسندگان English

Sajad Ranjbar 1
Hadi Khatibzadeh 2
Parviz Ahmadi 2
1 Higher Education Center of Eghlid
2 University of Zanjan
چکیده English

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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کلیدواژه‌ها English

 Geodesic
Metric segment
d-convex set
Metric convex hull
d-convex function
Extreme point
Continuity
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