Structure of a generalized class of weights satisfy weighted reverse Hölder’s inequality
Structure of a generalized class of weights satisfy weighted reverse Hölder’s inequality
Abstract In this paper, we will prove some fundamental properties of the power mean operator $$ \mathcal{M}_{p}g(t)= \biggl( \frac{1}{\Upsilon(t)} \int _{0}^{t} \lambda (s)g^{p} ( s ) \,ds \biggr) ^{1/p},\quad\text{for }t\in \mathbb{I}\subseteq \mathbb{R}_{+}, $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:mi>g</mml:mi> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mrow> …