Results 1 to 10 of about 169,237 (207)
Minimizing Uniformly Convex Functions by Cubic Regularization of Newton Method. [PDF]
J Optim Theory Appl, 2021 AbstractIn this paper, we study the iteration complexity of cubic regularization of Newton method for solving composite minimization problems with uniformly convex objective. We introduce the notion of second-order condition number of a certain degree and justify the linear rate of convergence in a nondegenerate case for the method with an adaptive ...
Doikov N, Nesterov Y.
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Sufficiency for Gaussian hypergeometric functions to be uniformly convex [PDF]
International Journal of Mathematics and Mathematical Sciences, 1999 Let F(a, b; c; z) be the classical hypergeometric function and f be a normalized analytic functions defined on the unit disk 𝒰. Let an operator Ia,b;c(f) be defined by [Ia,b;c(f)](z) = zF(a, b; c; z)*f(z). In this paper the authors identify two subfamilies of analytic functions ℱ1 and ℱ2 and obtain conditions on the parameters a, b, c such that f ∈ ℱ1 ...
Yong Chan Kim, S. Ponnusamy
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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 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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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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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 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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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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Mathematica Bohemica, 2021 The aim of this paper is to find the necessary and sufficient conditions and inclusion relations for Pascal distribution series to be in the classes SP_{p}( ,\b{eta}) and UCV_{p}( ,\b{eta}) of uniformly spirallike functions. Further, we consider properties of a special function related to Pascal distribution series.
Gangadharan Murugusundaramoorthy +2 more
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Generalized hypergeometric functions associated with k-uniformly convex functions
Computers & Mathematics with Applications, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gangadharan, A. +2 more
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