Norm Inequalities via Convex and Log-Convex Functions

• Autores: Conde, Cristian Marcelo; Minculete, Nicusor; Moradi, Hamid Reza; Sababheh, Mohammad
• Año de publicación: 2023
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: Mediterranean Journal Of Mathematics. Ene. 2023; 20(1): 1-21
• Materia: Inner Product Space; Triangle Inequality; Cauchy-Schwarz Inequality; Log-Convex Function; Matemáticas; Matemática Pura
• Institución: Universidad Nacional de General Sarmiento

Revista con referato
Fil: Conde, Cristian Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.
Fil: Conde, Cristian Marcelo. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
Fil: Minculete, Nicusor. Transilvania University; Rumania.
Fil: Moradi, Hamid Reza. Payame Noor University; Irán.
Fil: Sababheh, Mohammad. Princess Sumaya University For Technology; Jordania.
In this paper, we study the norm and skew angular distances in a normed space , where convex functions are used to obtain refinements and reverses of some outstanding results in the literature. For example, in this regard, we show that if are non-zero and if are such that , then where , and . Then we explain how this result extends some known results in the literature. Many other related results will be also shown. Then, with the theme of convexity, we employ a log-convex approach on certain matrix functions to obtain improvements and new sights of some matrix inequalities, including possible bounds of where A, B are positive definite matrices, X is an arbitrary matrix, is a unitarily invariant norm and Many other results involving matrix and scalar log-convex functions will be presented too.