Displaying similar documents to “Sharp Estimates For Some Integral Operators Of Convex Functions Of Order Alpha”

Sharp norm estimate of Schwarzian derivative for a class of convex functions

Stanisława Kanas, Toshiyuki Sugawa (2011)

Annales Polonici Mathematici

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We establish a sharp norm estimate of the Schwarzian derivative for a function in the classes of convex functions introduced by Ma and Minda [Proceedings of the Conference on Complex Analysis, Int. Press, 1992, 157-169]. As applications, we give sharp norm estimates for strongly convex functions of order α, 0 < α < 1, and for uniformly convex functions.

Banach spaces and operators which are nearly uniformly convex

Prus Stanisław

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CONTENTSIntroduction..............................................................................................5 I. Basic definitions and notation..............................................................6  M-bases and finite-dimensional decompositions....................................6  Some geometric properties of Banach spaces.......................................9 II. Constructions of equivalent norms.....................................................12 III. (p,q)-estimates...