Weighted \v{C}eby\v{s}ev Type Inequalities for Double Integrals and Application

The purpose of this article is to generalize \v{C}eby\v{s}ev type inequalities for double integrals involving a weight function.By using an integral transform that is a weighted Montgomery identity, we obtained a generalized form of weighted \v{C}eby\v{s}ev type inequalities in $L_m,\, m\geq ۱$ norm of differentiable functions. Also, we give some applications of the probability density function.

Keywords:

\v{C}eby\v{s}ev inequality , Weighted \v{C}eby\v{s}ev inequality , Montgomery identity , Probability density function