Add to ORKGsummary:We prove: If $A(n)$ and $G(n)$ denote the arithmetic and geometric means of the first $n$ positive integers, then the sequence $n\mapsto nA(n)/G(n)-(n-1)A(n-1)/G(n-1)$ $(n\geq 2)$ is strictly increasing and converges to $e/2$, as $n$ tends to $\infty $
AbstractLet ζ be the Riemann zeta function and δ(x)=1/(2x-1). For all x>0 we have(1-δ(x))ζ(x)+αδ(x)<...
In this note we investigate the positive integersnfor whichφ(n2)+σ2(n) is divisible byn2
AbstractA monotonicity result for the ratio between two generalized logarithmic means is established...
summary:We prove: If $A(n)$ and $G(n)$ denote the arithmetic and geometric means of the first $n$ po...
Abstract. Connections of an inequality of Klamkin with Stolarsky means and convexity are shown. An a...
In this paper refinements and converses of matrix forms of the geometric-arithmetic mean inequality ...
summary:There are many relations involving the geometric means $G_n(x)$ and power means $[A_n(x^{\ga...
We deduce an inequality using elementary methods which makes it possible to prove a conjecture reg...
In this article, we present four issues and provide a creative and concise proof for each of them. T...
AbstractIn this note we present some new and structural inequalities for digamma, polygamma and inve...
Rec ently, Sun defined a newsequence $a(n)= \sum_{k=0}^n {n\choose 2k}{2k\choose k}\frac{1}{2k-1} $,...
summary:Some generalizations of the Ostrowski inequality, the Milovanović-Pečarić-Fink inequality, t...
AbstractUsing Hayashi’s inequality, an Iyengar type inequality for functions with bounded second der...
We consider weighted arithmetic means as, for example, \(\alpha G+(1-\alpha)C,\) with \(\alpha\in(0,...
AbstractIn this short note, the authors give a proof of a certain geometric inequality conjecture of...
AbstractLet ζ be the Riemann zeta function and δ(x)=1/(2x-1). For all x>0 we have(1-δ(x))ζ(x)+αδ(x)<...
In this note we investigate the positive integersnfor whichφ(n2)+σ2(n) is divisible byn2
AbstractA monotonicity result for the ratio between two generalized logarithmic means is established...
summary:We prove: If $A(n)$ and $G(n)$ denote the arithmetic and geometric means of the first $n$ po...
Abstract. Connections of an inequality of Klamkin with Stolarsky means and convexity are shown. An a...
In this paper refinements and converses of matrix forms of the geometric-arithmetic mean inequality ...
summary:There are many relations involving the geometric means $G_n(x)$ and power means $[A_n(x^{\ga...
We deduce an inequality using elementary methods which makes it possible to prove a conjecture reg...
In this article, we present four issues and provide a creative and concise proof for each of them. T...
AbstractIn this note we present some new and structural inequalities for digamma, polygamma and inve...
Rec ently, Sun defined a newsequence $a(n)= \sum_{k=0}^n {n\choose 2k}{2k\choose k}\frac{1}{2k-1} $,...
summary:Some generalizations of the Ostrowski inequality, the Milovanović-Pečarić-Fink inequality, t...
AbstractUsing Hayashi’s inequality, an Iyengar type inequality for functions with bounded second der...
We consider weighted arithmetic means as, for example, \(\alpha G+(1-\alpha)C,\) with \(\alpha\in(0,...
AbstractIn this short note, the authors give a proof of a certain geometric inequality conjecture of...
AbstractLet ζ be the Riemann zeta function and δ(x)=1/(2x-1). For all x>0 we have(1-δ(x))ζ(x)+αδ(x)<...
In this note we investigate the positive integersnfor whichφ(n2)+σ2(n) is divisible byn2
AbstractA monotonicity result for the ratio between two generalized logarithmic means is established...