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In this paper, we obtain some new upper bounds for differantiable mappings whose q-th powers are geometrically convex and monotonically decreasing by using the H\"older inequality, Power mean inequality and properties of modulus.

Classical Analysis and ODEs · Mathematics 2013-12-31 M. Emin Özdemir

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,…

Functional Analysis · Mathematics 2016-06-28 Mohammad Sababheh

In this paper we present several new classes of logarithmically completely monotonic functions. Our functions have in common that they are defined in terms of the $q-$gamma and $q-$digamma functions. As an applications of this results, some…

Classical Analysis and ODEs · Mathematics 2015-12-21 Khaled Mehrez

We characterize real functions $f$ on an interval $(-\alpha,\alpha)$ for which the entrywise matrix function $[a_{ij}] \mapsto [f(a_{ij})]$ is positive, monotone and convex, respectively, in the positive semidefiniteness order. Fractional…

Functional Analysis · Mathematics 2007-10-09 Fumio Hiai

By making use of the familiar Mathieu series and its generalizations, the authors derive a number of new integral representations and present a systematic study of probability density functions and probability distributions associated with…

Classical Analysis and ODEs · Mathematics 2016-10-19 Zivorad Tomovski , Khaled Mehrez

In this paper, we establish some new integral inequalities for for m- and (alpha,m)-logarithmically convex functions.

Classical Analysis and ODEs · Mathematics 2012-11-29 Mevlut Tunc

This note deals with certain properties of convex functions. We provide results on the convexity of the set of minima of these functions, the behaviour of their subgradient set under restriction, and optimization of these functions over an…

Optimization and Control · Mathematics 2017-03-21 Miel Sharf , Daniel Zelazo

We study the convexity/concavity properties of the generalized $p$-trigonometric functions in the sense of P. Lindqvist with respect to the power means.

Classical Analysis and ODEs · Mathematics 2012-09-06 Barkat Ali Bhayo , Matti Vuorinen

In this paper, we study operator mean inequalities for the weighted arithmetic, geometric and harmonic means. We give a slight modification of Audenaert's result to show the relation between Kwong functions and operator monotone functions.…

Functional Analysis · Mathematics 2024-05-10 Nahid Gharakhanlu , Mohammad Sal Moslehian , Hamed Najafi

In this paper, additional properties of the lower gamma functions and the error functions are introduced and proven. In particular, we prove interesting relations between the error functions and Laplace transform.

Classical Analysis and ODEs · Mathematics 2015-02-17 Rami AlAhmad

Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime $(M,g_{\mu \nu})$ or an initial…

General Relativity and Quantum Cosmology · Physics 2009-10-07 Gary W. Gibbons , Akihiro Ishibashi

Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime $(M,g_{\mu \nu})$ or an initial…

Differential Geometry · Mathematics 2017-02-21 Gary W. Gibbons , Akihiro Ishibashi

We establish sharp inequalities involving the incomplete Beta and Gamma functions. These inequalities arise in the approximation of generalized Bernstein functions by higher order Thorin-Bernstein functions. Furthermore, new properties of a…

Classical Analysis and ODEs · Mathematics 2024-09-05 Stamatis Koumandos , Henrik Laurberg Pedersen

The paper studies logarithmic convexity and concavity of the generalized hypergeometric function with respect to simultaneous shift of several parameters. We use integral representations and properties of Meijer's $G$ function to prove…

Classical Analysis and ODEs · Mathematics 2016-11-22 S. I. Kalmykov , D. B. Karp

Motivated by existing results, we present some completely monotonic functions involving the polygamma functions.

Classical Analysis and ODEs · Mathematics 2010-12-03 Peng Gao

A class of functions involving the divided differences of the psi function and the polygamma functions and originating from Kershaw's double inequality are proved to be completely monotonic. As applications of these results, the…

Classical Analysis and ODEs · Mathematics 2011-05-13 Feng Qi , Bai-Ni Guo

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…

Classical Analysis and ODEs · Mathematics 2014-05-08 Feng Qi , Bai-Ni Guo

The authors establish the necessary and sufficient conditions under which certain combinations of Gaussian hypergeometric function and elementary function are monotone in the parameter, which generalize the recent results of generalized…

Classical Analysis and ODEs · Mathematics 2021-12-30 Qi Bao , Miao-Kun Wang , AND Song-Liang Qiu

In this paper our aim is to present some monotonicity and convexity properties for the one dimensional regularization of the Coulomb potential, which has applications in the study of atoms in magnetic fields and which is in fact a…

Classical Analysis and ODEs · Mathematics 2013-08-19 Árpád Baricz , Tibor K. Pogány

This study focuses on convex functions and their generalized. Thus, we start this study by giving the definition of convex functions and some of their properties and discussing a simple geometric property. Then we generalize E-convex…

Classical Analysis and ODEs · Mathematics 2017-04-27 Adem Kilicman , Wedad Saleh