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A Generalized Theory of Convexity

Proceedings of the London Mathematical Society, 1967
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Generalizations of convexity

1978
I consider four generalizations of the concept of a convex set in Rd. A subset X of R belongs to the family T(a) if for all x, y e X ax + (1 -a)y e X where a e R. Properties of elements of T(a) are considered in Chapter 1.Also in Chapter 1 a planar generalization of the family T(a) is considered.
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Convex Functions and Generalized Convex Functions

2023
Giorgio Giorgi   +2 more
openaire   +1 more source

Characterizations of generalized convexities via generalized directional derivatives

Numerical Functional Analysis and Optimization, 1998
Jean-Paul Penot, Pham Huu Sach
exaly  

Generalized convexities and generalized gradients based on algebraic operations

Journal of Mathematical Analysis and Applications, 2006
Panos M Pardalos   +2 more
exaly  

Generalized monotonicity and convexity of non-differentiable functions

Journal of Mathematical Analysis and Applications, 2003
Sanyang Liu, Liya Fan
exaly  

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