×

zbMATH — the first resource for mathematics

Characterizations of generalized convexities via generalized directional derivatives. (English) Zbl 0916.49015
Convexity, quasiconvexity, invexity and pseudoconvexity are characterized for a real-valued radially upper-semicontinuous function \(f\) on a topological vector space, in terms of appropriate properties of a bifunction which is majorized by the upper radial derivative of \(f\), and is so a sort of generalized derivative.

MSC:
49J52 Nonsmooth analysis
26B25 Convexity of real functions of several variables, generalizations
90C48 Programming in abstract spaces
90C26 Nonconvex programming, global optimization
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Anselone P.M., Prentice Hall. (1971)
[2] Appell J., Pac. Jour. Math. 115 pp 13– (1984)
[3] De Blasi F.S., Bull. Math. Soc. Roum. 21 pp 259– (1977)
[4] Dugundji J., Monografie Matematyczne (1982)
[5] Emmanuele G., Bull. Math. Soc. Roum 25 pp 353– (1981)
[6] DOI: 10.1016/0362-546X(95)00130-N · Zbl 0874.47035
[7] O’Regan D., Computers Math. Applic.
[8] O’Regan, D. ”Operator equations in Banach spaces relative to the weak topology”. to appear
[9] O’Regan, D. ”Fixed point theory for weakly contractive maps with applications to operator inclusions in Banach spaces relative to the weak topology”. to appear
[10] O’Regan, D. ”Nonlinear alternatives for multivalued maps with applications to operator inclusions in abstract spaces”. to appear
[11] DOI: 10.1006/jmaa.1994.1256 · Zbl 0856.47036
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.