Tmetoceratidae (Ammonitina) fauna from the Gerecse Mts (Hungary)

Abstract Taxonomic and stratigraphic problems of the family Tmetoceratidae and the genera Dumortieria, Catulloceras, Cotteswoldia, Pleydellia and Tmetoceras included in it are briefly discussed. Fifteen species of Tmetoceratidae are described and illustrated from the Upper Toarcian-Aalenian ammonite assemblages of the Gerecse Mts (NE Transdanubian Range, Hungary). The fauna described here is closely allied to the Mediterranean Province of the Mediterranean-Caucasian Realm

Convex Operators in Vector Optimization: Directional Derivatives and the Cone of Decrease Directions

The paper is devoted to the investigation of directional derivatives and the cone of decrease directions for convex operators on Banach spaces. We prove a condition for the existence of directional derivatives which does not assume regularity of the ordering cone K. This result is then used to prove that for continuous convex operators the cone of decrease directions can be represented in terms of the directional derivatices . Decrease directions are those for which the directional derivative lies in the negative interior of the ordering cone K. Finally, we show that the continuity of the convex operator can be replaced by its K-boundedness

Convex Operators in Vector Optimization: Directional Derivatives and the Cone of Decrease Directions

The paper is devoted to the investigation of directional derivatives and the cone of decrease directions for convex operators on Banach spaces. We prove a condition for the existence of directional derivatives which does not assume regularity of the ordering cone K. This result is then used to prove that for continuous convex operators the cone of decrease directions can be represented in terms of the directional derivatices . Decrease directions are those for which the directional derivative lies in the negative interior of the ordering cone K. Finally, we show that the continuity of the convex operator can be replaced by its K-boundedness

Convex Operators in Vector Optimization: Directional Derivatives and the Cone of Decrease Directions

The paper is devoted to the investigation of directional derivatives and the cone of decrease directions for convex operators on Banach spaces. We prove a condition for the existence of directional derivatives which does not assume regularity of the ordering cone K. This result is then used to prove that for continuous convex operators the cone of decrease directions can be represented in terms of the directional derivatives. Decrease directions are those for which the directional derivative lies in the negative interior of the ordering cone K. Finally, we show that the continuity of the convex operator can be replaced by its K-boundedness. Key words: Vector optimization, convex operator, directional derivative, decrease direction, normal cone, AMS Subject Classification: 90C29, 90C48 2 1. Introduction In optimization theory it is well known that convex functions as well as convex sets in play an important role. Convexity assumptions lead to significantly stronger reults than hold ..