Related papers: Some sharp inequalities involving Seiffert and oth…
In the paper, the authors find the best possible constants appeared in two inequalities for bounding the Seiffert mean by the linear combinations of the arithmetic, centroidal, and contra-harmonic means.
In the paper, by finding linear relations of differences between some means, the authors supply a unified proof of some double inequalities for bounding Neuman-S\'andor means in terms of the arithmetic, harmonic, and contra-harmonic means…
The current status concerning Hardy-type inequalities with sharp constants is presented and described in a unified convexity way. In particular, it is then natural to replace the Lebesgue measure $dx$ with the Haar measure $dx/x.$ There are…
We mainly establish a monotonicity property between some special Riemann sums of a convex function $f$ on $[a,b]$, which in particular yields that $\frac{b-a}{n+1}\sum_{i=0}^n f\left(a+i\frac{b-a}{n}\right)$ is decreasing while…
In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root-square means, etc. Some new means recently studied are also presented. Different kinds of refinement of inequalities among these means are…
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.
Motivared by Carleman's proof of the isoperimetric inequality in the plane, we study some sharp integral inequalities for harmonic functions on the upper halfspace. We also derive the regularity for nonnegative solutions of the associated…
In this note, we derive non trivial sharp bounds related to the weighted harmonic-geometric-arithmetic means inequalities, when two out of the three terms are known. As application, we give an explicit bound for the trace of the inverse of…
In this paper, we provide a concise proof of Oppenheim's double inequality relating to the cosine and sine functions. In passing, we survey this topic.
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 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…
In the paper, we establish an inequality involving the gamma and digamma functions and use it to prove the negativity and monotonicity of a function involving the gamma and digamma functions.
We prove a conjecture of Cuttler et al.~[2011] [A. Cuttler, C. Greene, and M. Skandera; \emph{Inequalities for symmetric means}. European J. Combinatorics, 32(2011), 745--761] on the monotonicity of \emph{normalized Schur functions} under…
An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.
The main goal of this article is to find the exact difference between a convex function and its secant, as a limit of positive quantities. This idea will be expressed as a convex inequality that leads to refinements and reversals of well…
In this paper, we present the greatest values $\alpha$, $\lambda$ and $p$, and the least values $\beta$, $\mu$ and $q$ such that the double inequalities $\alpha D(a,b)+(1-\alpha)H(a,b)<T(a,b)<\beta D(a,b)+(1-\beta) H(a,b)$, $\lambda…
In this paper, the authors present sharp approximations in terms of sine function and polynomials for the so-called Ramanujan constant (or the Ramanujan $R$-function) $R(a)$, by showing some monotonicity, concavity and convexity properties…
In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions…
Motivated by open questions in the papers " Refinements and sharpenings of some double inequalities for bounding the gamma function" and "Complete monotonicity and monotonicity of two functions defined by two derivatives of a function…
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…