Continuous generalized convex functions and their characterizations

Abstract

The notions of continuous (strictly) pseudoconvex functions and set-valued (strictly) pseudomonotone maps are introduced. Relations between these notions are given using an asymptotic mean value theorem. Characterizations of a continuous quasiconvex function are derived.

Keywords:

• Quasiconvex function
• Pseudoconvex function
• Pseudomonotone map
• Mean value theorem
• 1991 Mathematics Subject Classifications: 26A51
• 47H04

Acknowledgments

The author is most grateful to Dr. V. Jeyakumar for some discussions on the topic of this article. The work in this article was supported by a grant from the Research Grants Council of the Hong Kong Special Administration Region, China (PolyU 5145/02E).

Notes

Dedicated to V.F. Demyanov on the occasion of his 65th birthday.

Additional information

Notes on contributors

X. Q. Yang

Dedicated to V.F. Demyanov on the occasion of his 65th birthday.