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Uniformly convex and uniformly smooth convex functions [PDF]
Annales de la Faculté des sciences de Toulouse : Mathématiques, 1995 The duality between the uniform smoothness of the convex function \(f\) and the uniform convexity of its conjugate \(g\) is studied in the framework of Banach spaces in metric duality. Several characterizations of these notions are given using the subdifferentials of \(f\) and \(g.\) The paper is much related to reviewer's article [J. Math. Anal. Appl.
Azé, Dominique, Penot, Jean-Paul
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Absolutely convex, uniformly starlike and uniformly convex harmonic mappings [PDF]
Complex Variables and Elliptic Equations, 2016 In this paper, we prove necessary and sufficient conditions for a sense-preserving harmonic function to be absolutely convex in the open unit disk. We also estimate the coefficient bound and obtain growth, covering and area theorems for absolutely convex harmonic mappings.
Ponnusamy, Saminathan +2 more
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Uniformly convex functions II [PDF]
Annales Polonici Mathematici, 1993 For part I see the author in ibid. 57, No. 2, 165-175 (1992; Zbl 0760.30005). Let \({\mathcal P}\) be the family of holomorphic functions \(p\) defined on the unit disc \(\Delta=\{z:| z |0\) in \(\Delta\). The authors in [ibid. 57, No. 2, 165-175 (1992; Zbl 0760.30005)] considered the subfamily \[ PAR=\{p \in {\mathcal P}:p(\Delta) \subset \Omega ...
Ma, Wancang, Minda, David
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UNIFORMLY CONVEX-TRANSITIVE FUNCTION SPACES [PDF]
The Quarterly Journal of Mathematics, 2009 We introduce a property of Banach spaces called uniform convex-transitivity, which falls between almost transitivity and convex-transitivity. We will provide examples of uniformly convex-transitive spaces. This property behaves nicely in connection with some Banach-valued function spaces.
Rambla-Barreno, Fernando +2 more
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Uniformly convex functions [PDF]
Annales Polonici Mathematici, 1992 A function \(f(z)=z+a_ 2 z^ 2+a_ 3 z^ 3+\dots\) which is holomorphic on the unit disk \(\Delta=\{z\): \(| z|
Ma, Wancang, Minda, David
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Journal of Mathematical Analysis and Applications, 2022 Non-convex functions that yet satisfy a condition of uniform convexity for non-close points can arise in discrete constructions. We prove that this sort of discrete uniform convexity is inherited by the convex envelope, which is the key to obtain other remarkable properties such as the coercivity.
Grelier, G., Raja, M.
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UNIFORMLY CONVEX AND STARLIKE PROBABILITY DISTRIBUTION
South East Asian J. of Mathematics and Mathematical Sciences, 2023 The purpose of the present paper is to introduce k− uniformly convex and k− uniformly starlike discrete probability distributions and obtain some results regarding moments, factorial moments and moment generating functions for these distributions.
Porwal, Saurabh +3 more
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Uniformly convex totally ordered sets [PDF]
Proceedings of the American Mathematical Society, 1975 Since a uniformly convex totally ordered set is a uniform lattice, its uniform completion is totally ordered in a natural way. The assumption of uniform convexity is a small restriction because every nearly uniform ordered space is uniformly convex.
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Interpolation of Uniformly Convex Banach Spaces [PDF]
Proceedings of the American Mathematical Society, 1982 If A 0 {A_0} and A 1 {A_1} are a compatible couple of Banach spaces, one of which is uniformly convex, then the complex interpolation spaces [ A 0 ,
Cwikel, Michael, Reisner, Shlomo
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On uniformly close‐to‐convex functions and uniformly quasiconvexfunctions [PDF]
International Journal of Mathematics and Mathematical Sciences, 2003 Two new subclasses of uniformly convex and uniformly close‐to‐convex functions are introduced. We obtain inclusion relationships and coefficient bounds for these classes.
K. G. Subramanian +2 more
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