Related papers: Operator convex functions and their applications
In this paper, we establish new general inequality for convex functions. Then we apply this inequality to obtain the midpoint, trapezoid and averaged midpoint-trapezoid integral inequality. Also, some applications for special means of real…
To study operator algebras with symmetries in a wide sense we introduce a notion of {\em relative convolution operators} induced by a Lie algebra. Relative convolutions recover many important classes of operators, which have been already…
We analyze a class of sublinear functionals which characterize the interior and the exterior of a convex cone in a normed linear space.
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.
A Minkowski symmetral of an $\alpha$-concave function is introduced, and some of its fundamental properties are derived. It is shown that for a given $\alpha$-concave function, there exists a sequence of Minkowski symmetrizations that…
In this article, we present exponential-type inequalities for positive linear mappings and Hilbert space operators, by means of convexity and the Mond-Pe\v cari\'c method. The obtained results refine and generalize some known results. As an…
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…
In this paper we consider some properties of the initial logarithmic coefficients for inverse functions of functions univalent in the unit disc. The case of convex functions is treated separately. We give estimate, in some cases sharp, of…
A classification of $\operatorname{SL}(n)$ and translation covariant Minkowski valuations on log-concave functions is established. The moment vector and the recently introduced level set body of log-concave functions are characterized.…
We introduce floating bodies for convex, not necessarily bounded subsets of $\mathbb{R}^n$. This allows us to define floating functions for convex and log concave functions and log concave measures. We establish the asymptotic behavior of…
In this paper we introduce and study a new sequence of positive linear operators acting on function spaces defined on a convex compact subset. Their construction depends on a given Markov operator, a positive real number and a sequence of…
The authors define a class of functions on Riemannian manifolds, which is called geodesic semilocal E-preinvex functions, as a generalization of geodesic semilocal E-convex and geodesic semi E-preinvex functions and some of its properties…
In this paper, we first prove two new identities for multiplicative differentiable functions. Based on this identity, we establish a midpoint and trapezoid type inequalities for multiplicatively convex functions. Applications to special…
We obtain new concavity results, up to a suitable transformation, for a class of quasi-linear equations in a convex domain involving the $p$-Laplace operator and a general nonlinearity satisfying concavity type assumptions. This provides an…
In this paper, the notation of strongly log-convex functions with respect to c>0 is introduced and versions of Hermite Hadamard-type inequalities for strongly logarithmic convex functions are established.
In this paper, we develop a basic theory of Orlicz affine and geominimal surface areas for convex and $s$-concave functions. We prove some basic properties for these newly introduced functional affine invariants and establish related…
New perspectives, proofs, and some extensions of known results are presented concerning the behavior of the Fitzpatrick function of a monotone type operator in the general context of a locally convex space.
In this paper, we introduce a new generalized class of analytic functions involving the Mittag-Leffler operator and Bazilevi\u{c} functions. We examine inclusion properties, radius problems and an application of the generalized…
The author introduce the concept of harmonically convex functions and establish some Hermite-Hadamard type inequalities of these classes of functions
We present a Diaz--Metcalf type operator inequality as a reverse Cauchy-Schwarz inequality and then apply it to get the operator versions of P\'{o}lya-Szeg\"{o}'s, Greub-Rheinboldt's, Kantorovich's, Shisha-Mond's, Schweitzer's, Cassels' and…