Related papers: Logarithmic convexity of Gini means
In this paper, we study some properties such as the monotonicity, logarithmically complete monotonicity, logarithmic convexity, and geometric convexity, of the combinations of gamma function and power function. The results we obtain…
In this paper we study the convexity and concavity properties of generalized trigonometric and hyperbolic functions in case of Logarithmic mean.
We simplify the proof of some widely used theoretical theorems, extending their applicability, while correcting some erroneous results. We also generalize key results and present new results that contribute to the development of the theory.…
In the paper, we present a monotonicity result of a function involving the gamma function and the logarithmic function, refine a double inequality for the gamma function, and improve some known results for bounding the gamma function.
Some mathematical inequalities among various weighted means are studied. Inequalities on weighted logarithmic mean are given. Besides, the gap in Jensen's inequality is studied as a convex function approach. Consequently, some non-trivial…
The purpose of this paper is to introduce the logarithmic mean of two convex functionals that extends the logarithmic mean of two positive operators. Some inequalities involving this functional mean are discussed as well. The operator…
In this paper, some monotonicity and concavity results of several functions involving the psi and polygamma functions are proved, and then some known inequalities are extended and generalized.
In this paper, we got some refinements of the norm inequalities related to the Heinz mean and logarithmic mean.
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…
In the paper, the authors concisely survey and review some functions involving the gamma function and its various ratios, simply state their logarithmically complete monotonicity and related results, and find necessary and sufficient…
We characterize the convexity of functions and the monotonicity of vector fields on metric measure spaces with Riemannian Ricci curvature bounded from below. Our result offers a new approach to deal with some rigidity theorems such as…
This article employs techniques from convex analysis to present characterizations of (maximal) $n-$monotonicity, similar to the well-established characterizations of (maximal) monotonicity found in the existing literature. These…
We consider Gini means with short biographical information and propose a new proof of the main inequality for these means. Also some applications of Gini and other means are considered to polymer chemistry.
In this note we study the monotonicity of the function $x\mapsto \psi(1 +bx)^a/\psi(1 + ax)^b$. We also give the several inequalities involving the psi function, whic is the logarithmic derivative of the gamma function.
In the paper, the authors review origins, motivations, and generalizations of a series of inequalities involving several exponential functions and sums, establish three new inequalities involving finite exponential functions and sums by…
In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, logarithmic means, etc. Inequalities involving logarithmic mean with differences among other means are presented
Let $\Omega_n$ stand for the volume of the unit ball in $\mathbb{R}^n$ for $n\in\mathbb{N}$. In the present paper, we prove that the sequence $\Omega_{n}^{1/(n\ln n)}$ is logarithmically convex and that the sequence…
In this paper, we give more general definitions of weighted means and MN-convex functions. Using these definitions, we also obtain some generalized results related to properties of MN-convex functions. The importance of this study is that…
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 describe s-logarithmically convex functions in the first and second sense which are connected with the ordinary logatihmic convex and s-convex in the first and second sense. Afterwards, some new inequalities related to…