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Ona-Wright convexity and the converse of Minkowski's inequality
Authors:Janusz Matkowski
Institution:(1) Department of Mathematics, Technical University, Willowa 2, PL-43-309 Bielsko-Biala, Poland
Abstract:Summary Leta isin (0, 1/2] be fixed. A functionf satisfying the inequalityf(ax + (1 – a)y) + f((1 – a)x + ay) les f(x) + f(y), called herea-Wright convexity, appears in connection with the converse of Minkowski's inequality. We prove that every lower semicontinuousa-Wright convex function is Jensen convex and we pose an open problem. Moreover, using the fact that 1/2-Wright convexity coincides with Jensen convexity, we prove a converse of Minkowski's inequality without any regularity conditions.
Keywords:Primary: 26A51  26B25  26D15  46E30  39C05  Secondary: 26A18  39B10
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