Add to ORKGAbstract. If f is a positive integrable function, then it is well-known that for real numbers p and q, q ≤ p, the ratio of the p-power integral mean of f by the q-power integral mean is greater than or equal to 1. Different authors have given reverse inequalities for this ratio. Here we present various upper bounds for this ratio for a wider class of weighted power means and functions. These results are extensions of results of Muckenhoupt, Nania and Alzer. 1
AbstractIn this paper, we show that the ν-weighted arithmetic mean is greater than the product of th...
AbstractWe establish the inequality [equation] where α=CK,n=p/q,q−1+(u′(x)R(x)/u2(x)r(x))≥q/KandR(x)...
In this paper, we show that the ν-weighted arithmetic mean is greater than the product of the ν-weig...
AbstractA consequence of Hölder's inequality is the well-known inequality between means of orderspan...
Abstract This note aims to generalize the reverse weighted arithmetic–geometric mean inequality of n...
AbstractWe present an upper bound for the ratio [formula], where f is a positive decreasing function...
[[abstract]]We establish the inequality [equation] where α = CK,n = p/q,q − 1 + (u′(x)R(x)/u2(x)r(x)...
For , the power mean of order of two positive numbers and is defined by , for , and , for...
AbstractWe introduce a bound M of f, ‖f‖∞⩽M⩽2‖f‖∞, which allows us to give for 0⩽p<∞ sharp upper bou...
For , the power mean of order of two positive numbers and is defined by . In this paper, we...
AbstractIn this paper we gave a generalization of power means which include positive nonlinear funct...
For every given real value of the ratio μ := AX/GX\u3e 1 of the arithmetic and geometric means of a ...
In this paper, a best generalization of the reverse extended Hardy’s integral inequality is given by...
We present three inequalities involving the power mean Mp(a, b) =( ap 2 + bp 2)1/p of order p (p = ...
In the article, an integral inequality for the ratios of the arithmetic means of functions with a po...
AbstractIn this paper, we show that the ν-weighted arithmetic mean is greater than the product of th...
AbstractWe establish the inequality [equation] where α=CK,n=p/q,q−1+(u′(x)R(x)/u2(x)r(x))≥q/KandR(x)...
In this paper, we show that the ν-weighted arithmetic mean is greater than the product of the ν-weig...
AbstractA consequence of Hölder's inequality is the well-known inequality between means of orderspan...
Abstract This note aims to generalize the reverse weighted arithmetic–geometric mean inequality of n...
AbstractWe present an upper bound for the ratio [formula], where f is a positive decreasing function...
[[abstract]]We establish the inequality [equation] where α = CK,n = p/q,q − 1 + (u′(x)R(x)/u2(x)r(x)...
For , the power mean of order of two positive numbers and is defined by , for , and , for...
AbstractWe introduce a bound M of f, ‖f‖∞⩽M⩽2‖f‖∞, which allows us to give for 0⩽p<∞ sharp upper bou...
For , the power mean of order of two positive numbers and is defined by . In this paper, we...
AbstractIn this paper we gave a generalization of power means which include positive nonlinear funct...
For every given real value of the ratio μ := AX/GX\u3e 1 of the arithmetic and geometric means of a ...
In this paper, a best generalization of the reverse extended Hardy’s integral inequality is given by...
We present three inequalities involving the power mean Mp(a, b) =( ap 2 + bp 2)1/p of order p (p = ...
In the article, an integral inequality for the ratios of the arithmetic means of functions with a po...
AbstractIn this paper, we show that the ν-weighted arithmetic mean is greater than the product of th...
AbstractWe establish the inequality [equation] where α=CK,n=p/q,q−1+(u′(x)R(x)/u2(x)r(x))≥q/KandR(x)...
In this paper, we show that the ν-weighted arithmetic mean is greater than the product of the ν-weig...