Bivariate Chebyshev Type Inequalities for Alpha Diamond Integrals via Time Scale Calculus

Abstract

In this article, some generalizations of inequalities involving Chebyshev functional depending upon two parameters, for the class of twice differentiable functions on time scales, are studied. In order to reach the milestone, some preliminary identities are introduced involving delta and nabla integrals simultaneously. By utilizing these identities, Chebyshev type inequalities are obtained for diamond alpha integrals. Special cases are also deduced to obtain connection with existing literature.