A new reverse half-discrete Mulholland-type inequality with a nonhomogeneous kernel

Abstract

AbstractIn this paper, a new reverse half-discrete Mulholland-type inequality with the nonhomogeneous kernel of the form $h(v(x)\ln n)$ h ( v ( x ) ln n ) and the best possible constant factor is obtained by using the weight functions and the technique of real analysis. The equivalent reverses are considered. As corollaries, we deduce some new equivalent reverse inequalities with the homogeneous kernel of the form $k_{\lambda }(v(x),\ln n)$ k λ ( v ( x ) , ln n ) . A few particular cases are provided. Our new reverse half-discrete Mulholland-type inequality which has a nonhomogeneous kernel is more general than in the previous homogeneous kernel work. The harmonized integration will have more applications.