Hyperbolically Convex Functions
Zeinab Mohamed Yehia Youssef;
Abstract
The convexity of functions plays a central role in many various elds,
such as in economics, mechanics, biological system, optimization, and
other areas of applied mathematics. Throughout this thesis, let I be a
nonempty, connected, and bounded subset of R. A real valued function
f(x) of a single real variable x de ned on I is said to be convex if for
all u, v 2 I and 2 [0; 1] one has the inequality:
f( u + (1 )v) f(u) + (1 )f(v): (1)
At the beginning of the 20th century, many generalizations of convexity
were extensively introduced and investigated in number of ways
by numerous authors in the past and present. One way to generalize
the de nition of a convex function was to relax the convexity condition
1(for a comprehensive review, see the monographs [21]).
such as in economics, mechanics, biological system, optimization, and
other areas of applied mathematics. Throughout this thesis, let I be a
nonempty, connected, and bounded subset of R. A real valued function
f(x) of a single real variable x de ned on I is said to be convex if for
all u, v 2 I and 2 [0; 1] one has the inequality:
f( u + (1 )v) f(u) + (1 )f(v): (1)
At the beginning of the 20th century, many generalizations of convexity
were extensively introduced and investigated in number of ways
by numerous authors in the past and present. One way to generalize
the de nition of a convex function was to relax the convexity condition
1(for a comprehensive review, see the monographs [21]).
Other data
| Title | Hyperbolically Convex Functions | Other Titles | الدوال المحدبة زائديًا | Authors | Zeinab Mohamed Yehia Youssef | Issue Date | 2018 |
Recommend this item
Similar Items from Core Recommender Database
Items in Ain Shams Scholar are protected by copyright, with all rights reserved, unless otherwise indicated.