Related papers: The function $(b^x-a^x)/x$: Logarithmic convexity …
In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation,…
Using calculus we show how to prove some combinatorial inequalities of the type log-concavity or log-convexity. It is shown by this method that binomial coefficients and Stirling numbers of the first and second kinds are log-concave, and…
Our primary aim is to explore a sufficient condition for the class of meromorphically convex functions of order $\alpha$, where $0 \leq \alpha < 1$. The investigation will focus on studying a class of continuous functions defined on…
The theory of abstract convexity, also known as convexity without linearity, is an extension of the classical convex analysis. There are a number of remarkable results, mostly concerning duality, and some numerical methods, however, this…
We study concavity properties of positive solutions to the Logarithmic Schr\"odinger equation $-\Delta u=u\, \log u^2$ in a general convex domain with Dirichlet conditions. To this aim, we analyse the auxiliary Lane-Emden problems $-\Delta…
We present an elementary proof of a conjecture proposed by I. Rasa in 2017 which is an inequality involving Bernstein basis polynomials and convex functions. It was affirmed in positive by A. Komisarski and T. Rajba very recently by the use…
The main purpose of this paper is to determine the radii of starlikeness and convexity of the generalized $\emph{k}-$Bessel functions for three different kinds of normalization by using their Hadamard factorization in such a way that the…
We prove the logarithmic convexity of certain quantities, which measure the quadratic exponential decay at infinity and within two characteristic hyperplanes of solutions of Schr\"odinger evolutions. As a consequence we obtain some…
We investigate metric projections and distance functions referring to convex bodies in finite-dimensional normed spaces. For this purpose we identify the vector space with its dual space by using, instead of the usual identification via the…
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…
Let $\mathcal{A}$ denote the class of functions $f$ that are analytic in the open unit disk $\mathbb{D}$ and satisfy the normalization conditions $f(0) = 0$ and $f'(0) = 1$. This paper investigates the inverse logarithmic coefficients…
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 papaer, we put forward some new definitions and integral inequalities by using fairly elementary analysis.
The study of convex functions - in particular, of their optimization (really minimization) is one of the most important fields of applied mathematics. Convexity seems to be one of those incredibly well-chosen hypotheses which is just…
We give a statement on extension with estimates of convex functions defined on a linear subspace, inspired by similar extension results concerning metrics on positive line bundles
Matrix versions of some basic convexity inequalities are given. Further results on the same topic are proved in the recent papers on arxiv: 1. Hermitian operators and convex functions, 2. A concavity inequality for symmetric norms, 3.…
We discuss a rather general condition under which the inequality of Jensen works for certain convex combinations of points not all in the domain of convexity of the function under attention. Based on this fact, an extension of the…
Using convexity and superquadracity we extend in this paper Euler Lagrange identity, Bohr's inequalitiy and the triangle inequality.
In this article, logarithmically complete monotonicity properties of some functions such as $\frac1{[\Gamma(x+1)]^{1/x}}$, $\frac{[{\Gamma(x+\alpha+1)}]^{1/(x+\alpha)}}{[{\Gamma(x+1)}]^{1/x}}$, $\frac{[\Gamma(x+1)]^{1/x}}{(x+1)^\alpha}$ and…
In the paper, the authors establish an inequality involving exponential functions and sums, introduce a ratio of many gamma functions, discuss properties, including monotonicity, logarithmic convexity, (logarithmically) complete…