Related papers: The logarithmic mean of two convex functionals
In this paper our aim is to prove some monotonicity and convexity results for the modified Struve function of the second kind by using its integral representation. Moreover, as consequences of these results, we present some functional…
This paper investigates the generalized beta-logarithmic matrix function (GBLMF),which combines the extended beta matrix function and the logarithmic mean. The study establishes essential properties of this function, including functional…
Operator convex functions defined on the positive half-line play a prominent role in the theory of quantum information, where they are used to define quantum $f$-divergences. Such functions admit integral representations in terms of…
In this article, we employ a standard convex argument to obtain new and refined inequalities related to the matrix mean of two accretive matrices, the numerical radius and the Tsallis relative operator entropy.
In this article, we prove that convex functions and log-convex functions obey certain general refinements that lead to several refinements and reverses of well known inequalities for matrices, including Young's inequality, Heinz inequality,…
In this work, an operator superquadratic function (in operator sense) for positive Hilbert space operators is defined. Several examples with some important properties together with some observations which are related to the operator…
A considerable amount of literature in the theory of inequality is devoted to the study of Jensen's and Young's inequality. This article presents a number of new inequalities involving the log-convex functions and the geometrically convex…
In this paper, we got some refinements of the norm inequalities related to the Heinz mean and logarithmic mean.
It is proven that the logarithmic negativity does not increase on average under positive partial transpose preserving (PPT) operation including subselection (a set of operations that incorporate local operations and classical communication…
Jensen's operator inequality for convexifiable functions is obtained. This result contains classical Jensen's operator inequality as a particular case. As a consequence, a new refinement and a reverse of Young's inequality is given.
In the present paper two certain subclasses of the starlike functions associated with the vertical strip are considered. The main aim of this paper is to investigate some basic properties of these classes such as, subordination relations,…
We derive two types of representation results for increasing convex functionals in terms of countably additive measures. The first is a max-representation of functionals defined on spaces of real-valued continuous functions and the second a…
In this paper, authors generalize logarithmic mean $L$, Neuman-S\'andor $M$, two Seiffert means $P$ and $T$ as an application of generalized trigonometric and hyperbolic functions. Moreover, several two-sided inequalities involving these…
Given an operator convex function $f(x)$, we obtain an operator-valued lower bound for $cf(x) + (1-c)f(y) - f(cx + (1-c)y)$, $c \in [0,1]$. The lower bound is expressed in terms of the matrix Bregman divergence. A similar inequality is…
In this paper we extend some notions, previously defined for log-concave functions, to the larger domain of so-called {\alpha}-concave functions. We begin with a detailed discussion of support functions - first for log-concave functions,…
In this paper we introduce the concept of quadratic operator perspective for a continuous function {\Phi} defined on the positive semi-axis of real numbers. This generalize the quadratic weighted operator geometric mean and the quadratic…
This is a survey paper concerning some theorems on stochastic convex ordering and their applications to functional inequalities for convex functions. We present the recent results on those subjects
We prove Lieb type convexity and concavity results for trace functionals associated with positive operator monotone (decreasing) functions and certain monotone concave functions. This gives a partial generalization of Hiai's recent work on…
The logarithmic coefficients $\gamma_n$ of an analytic and univalent function $f$ in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$ with the normalization $f(0)=0=f'(0)-1$ are defined by $\log \frac{f(z)}{z}= 2\sum_{n=1}^{\infty}…
We consider an optimization problem with positively homogeneous functions in its objective and constraint functions. Examples of such positively homogeneous functions include the absolute value function and the $p$-norm function, where $p$…