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Uma introdução às funções convexas
(Universidade Tecnológica Federal do ParanáCuritibaBrasilPrograma de Pós-Graduação em Matemática em Rede NacionalUTFPR, 2018-12-07)
This dissertation presents an introduction to convex functions of one real variable. After studying the concept of convex set, the notion of convex function is
considered. Several theoretical results related to characterizations ...
Hermite-hadamard inequalities type for raina’ fractional integral operator using η−convex functions
(Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica., 2019)
Subdifferential of the supremum function: moving back and forth between continuous and non-continuous settings
(Springer, 2020)
In this paper we establish general formulas for the subdifferential of the pointwise supremum of convex functions, which cover and unify both the compact continuous and the non-compact non-continuous settings. From the ...
Best proximity pairs in uniformly convex spaces
(Instittute of Mathematics, 2008-12)
In this paper we prove existence theorems of best proximity pairs in uniformly convex spaces, using a fixed point theorem for Kakutani factorizable multifunctions.
SCHWARZIAN DERIVATIVES OF CONVEX MAPPINGS
(SUOMALAINEN TIEDEAKATEMIA, 2011)
A simple proof is given for Nehari's theorem that an analytic function f which maps the unit disk onto a convex region has Schwarzian norm parallel to f parallel to <= 2. The inequality in sharper form leads to the conclusion ...
Valadier-like formulas for the supremum function I
(Heldermann Verlag, 2018)
We generalize and improve the original characterization given by Valadier [18, Theorem 1] of the subdifferential of the pointwise supremum of convex functions, involving the subdifferentials of the data functions at nearby ...
Characterizing the Convexity of Joint-Range for a Pair of Inhomogeneous Quadratic Functions and Strong Duality
(2016)
We establish various extensions of the convexity Dines theorem for a (joint-range) pair of inhomogeneous quadratic functions. If convexity fails we describe those rays for which the sum of the joint-range and the ray is ...