Monotonic analysis over cones : III
- Authors: Dutta, J. , Martinez-Legaz, Juan , Rubinov, Alex
- Date: 2008
- Type: Text , Journal article
- Relation: Journal of Convex Analysis Vol. 15, no. 3 (2008), p. 561-579
- Full Text: false
- Reviewed:
- Description: This paper studies the class of increasing and co-radiant (ICR) functions over a cone equipped with an order relation which agrees with the conic structure. In particular, a representation of ICR functions as abstract convex functions is provided. This representation suggests the introduction of some polarity notions between sets. The relationship between ICR functions and increasing positively homogeneous functions is also shown.
- Description: C1
Hermite-Hadamard-type inequalities for increasing convex-along-rays function
- Authors: Rubinov, Alex , Dragomir, S. S , Dutta, J.
- Date: 2004
- Type: Text , Journal article
- Relation: Analysis Vol. 24, no. 2 (2004), p. 171-181
- Full Text: false
- Reviewed:
- Description: C1
- Description: 2003000933
Monotonic analysis over cones : I
- Authors: Dutta, J. , Martinez-Legaz, Juan , Rubinov, Alex
- Date: 2004
- Type: Text , Journal article
- Relation: Optimization Vol. 53, no. 2 (2004), p. 129-146
- Full Text: false
- Reviewed:
- Description: In this article, we study increasing and positively homogeneous functions defined on convex cones of locally convex spaces. This work is the first part in a series of studies to have a general view of the emerging area of Monotonic Analysis. We develop a general notion of so-called elementary functions, so that the generalized increasing and positively homogeneous functions can be represented as upper-envelopes of families of such functions. We also study many other associated properties like the description of support sets and normal and co-normal sets in a very general setting.
- Description: C1
- Description: 2003000930
Monotonic analysis over cones : II
- Authors: Dutta, J. , Martinez-Legaz, Juan , Rubinov, Alex
- Date: 2004
- Type: Text , Journal article
- Relation: Optimization Vol. 53, no. 5-6 (2004), p. 529-547
- Full Text: false
- Reviewed:
- Description: In this article, we study the class of increasing and convex along rays (ICAR) functions over a cone. Apart from studying its basic properties, we study them from the point of view of Abstract Convexity. Further, we study the relation between the ICAR and Lipschitz functions and the properties under which an ICAR function has a Lipschitz behaviour. We also study the class of decreasing and convex along rays functions (DCAR).
- Description: C1
- Description: 2003000931
Hadamard type inequality for quasiconvex functions in higher dimensions
- Authors: Rubinov, Alex , Dutta, J.
- Date: 2002
- Type: Text , Journal article
- Relation: Journal of Mathematical Analysis and Applications Vol. 270, no. 1 (2002), p. 80-91
- Full Text: false
- Reviewed:
- Description: In this article we study a Hadamard type inequality for nonnegative evenly quasiconvex functions. The approach of our study is based on the notion of abstract convexity. We also provide an explicit calculation to evaluate the asymptotically sharp constant associated with the inequality over a unit square in the two-dimensional plane. © 2002 Elsevier Science (USA). All rights reserved.
- Description: 2003000149