Related papers: Lieb type convexity for positive operator monotone…

Recently, the authors studied the connection between each maximal monotone operator T and a family H(T) of convex functions. Each member of this family characterizes the operator and satisfies two particular inequalities. The aim of this…

In this paper, we obtained some inequalities for \phi_{s}-convex function, \phi-Godunova-Levin function, \phi-P-function and log-\phi-convex function. Finally, we defined the class of \phi-quasi-convex functions and we examined some…

Some Tur\'an type inequalities for Struve functions of the first kind are deduced by using various methods developed in the case of Bessel functions of the first and second kind. New formulas, like Mittag-Leffler expansion, infinite product…

We discuss the following question: For a function f of two or more variables which is convex in the directions of coordinate axes, how can its trace g(x) = f(x, x, ..., x) look like? In the two-dimensional case, we provide some necessary…

We revisit and improve joint concavity/convexity and monotonicity properties of quasi-entropies due to Petz in a new fashion. Then we characterize equality cases in the monotonicity inequalities (the data-processing inequalities) of…

We employ techniques from optimal transport in order to prove decay of transfer operators associated to iterated functions systems and expanding maps, giving rise to a new proof without requiring a Doeblin-Fortet (or Lasota-Yorke)…

In this paper we prove some monotonicity, log--convexity and log--concavity properties for the Volterra and incomplete Volterra functions. Moreover, as consequences of these results, we present some functional inequalities (like Tur\'an…

We demonstrate three properties conjectured to hold for a certain function by Levin (2025) in a study of the blimpy graphical shape of the number of bit strings with a given score under an interesting scoring system. The properties include…

In this paper, some Jensen's type inequalities between quaternionic bounded selfadjoint operators on quaternionic Hilbert spaces are proved, using a log-convex function. Also, by applying a specific log-convex function, some particular…

This note aims to present novel positive linear operators involving the Wright function. Furthermore, the present research established the moments of these newly defined operators and estimated the convergence rate using the classical…

We prove a matrix trace inequality for completely monotone functions and for Bernstein functions. As special cases we obtain non-trivial trace inequalities for the power function x->x^q, which for certain values of q complement McCarthy's…

A general method for proving continuity of the von Neumann entropy on subsets of positive trace-class operators is considered. This makes it possible to re-derive the known conditions for continuity of the entropy in more general forms and…

A famous result of Lieb establishes that the map $(A,B) \mapsto \text{tr}\left[K^* A^{1-t} K B^t\right]$ is jointly concave in the pair $(A,B)$ of positive definite matrices, where $K$ is a fixed matrix and $t \in [0,1]$. In this paper we…

We quickly review and make some comments on the concept of convexity in metric spaces due to Takahashi. Then we introduce a concept of convex structure based convexity to functions on these spaces and refer to it as $W-$convexity.…

We investigate Lagrangian duality for nonconvex optimization problems. To this aim we use the $\Phi$-convexity theory and minimax theorem for $\Phi$-convex functions. We provide conditions for zero duality gap and strong duality. Among the…

We use relative trace formula to prove a non-vanishing result and a subconvexity result for the twisted base change $L$-functions associated to Hilbert modular forms whose local components at ramified places are some supercuspidal…

In this paper, we introduce the concept of operator arithmetic-geometrically convex functions for positive linear operators and prove some Hermite-Hadamard type inequalities for these functions. As applications, we obtain trace inequalities…

We study convexity or concavity of certain trace functions for the deformed logarithmic and exponential functions, and obtain in this way new trace inequalities for deformed exponentials that may be considered as generalizations of…

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…

This paper is about the technique of {\em shadow variables} that was used in the theory of monotone operators. In this paper, we use it to show that certain results that were originally proved for lower semicontinuous convex functions are…