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
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