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Abstract
In this paper some relations between strong pseudo-convexity and other generalized convexity-properties of mappings (convex-likeness, quasi -convexity) into Banach-spaces are described. Furthermore necessary and sufficient conditions for the strong pseudo-convexity of a mapping are presented. Especially, sufficient conditions for the strong pseudo-convexity of composite mappings are proved. Applying these results a correct ion of a direct duality theorem given by Chandra and Lata is formulated.