Cauchy and Pólya-Szeg? type inequalities involving two linear isotonic functionals

摘要

We consider inequalities which involve two linear isotonic functionals. We give two variants of the Cauchy inequality and few P′ olya-Szeg" o type inequalities in which functions with variable bounds occurred. With help of these inequalities we are able to obtain a new bound for the Chebyshev difference and give some particular cases. Connections of the presented results with earlier results involving fractional integrals are also pointed out.