Approximation of the Cubic Functional Equations in Lipschitz Spaces

Let G be an Abelian group and let ρ : G×G→[0,∞) be a metric on GLet E be a normed spaceWe prove that under some conditions if f : G→E is an odd function and Cx : G→E defined by Cx(y) := 2 f(x + y) +2 f(x-y) + 12 f(x)-f(2x + y)-f(2x-y)is a cubic function for all x∈G, then there exists a cubic function C : G→E such that f-C is LipschitzMoreover, we investigate the stability of cubic functional equation2 f(x + y) + 2 f(x-y) + 12 f(x)-f(2x + y)-f(2x-y) = 0 on Lipschitz spaces.     

Equivalence relations among inequalities for some relative operator entropies

Positivity - The relative operator entropy has properties like operator means. In addition, the relative operator entropy has entropy-like properties. In this paper, we prove a Loewner–Heinz...     

The n-Valent Convexity of Frasin Integral Operators

Ukrainian Mathematical Journal - Let fi, i 2 {1, 2, . . . ,k}, be an analytic function on the unit disk in the complex plane of the form fi(z) = zn + ai,n+1zn+1 + . . . , n �� ℕ...     

On operator inequalities of some relative operator entropies

In our recent paper, we introduced the notions of relative operator (α,β)$(\alpha ,\beta )$-entropy and Tsallis relative operator (α,β)$(\alpha ,\beta )$-entropy as a parameter extensions of relative operator entropy and Tsallis relative operator entropy. In this paper, we give upper and lower bounds of these new notions according to operator (α,β)$(\alpha ,\beta )$-geometric mean introduced in Nikoufar et al. (2013) [14].     

STABILITY OF GENERALIZED DERIVATIONS ON HILBERT C＊-MODULES ASSOCIATED WITH A PEXIDERIZED CAUCHY-JENSEN TYPE FUNCTIONAL EQUATION＊

In this article,we introduce the notion of generalized derivations on Hilbert C*-modules.We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized ...     

The converse of the Loewner–Heinz inequality via perspective

The Loewner–Heinz inequality is not only the most essential one in operator theory, but also a fundamental tool for treating operator inequalities. The aim of this paper is to investigate the converse of the Loewner–Heinz inequality in the view point of perspective and generalized perspective of operator monotone and multiplicative functions. Indeed, we give perspective inequalities equivalent to the Loewner–Heinz inequality.     

The simplest proof of Lieb concavity theorem

In this paper, by applying jointly concavity and jointly convexity of generalized perspective of some elementary functions, we give the simplest proof of the well-known Lieb concavity theorem and Ando convexity theorem.