Some new bounds of Chebyshev and Grüss-type functionals on time scales

Abstract

In this work, Korkine and Sonin's identities are defined on arbitrary time scales. These identities are utilized to establish the Chebyshev and Grüss-type inequalities on time scales. By applying these inequalities, we determine the bounds of the remainders in Montgomery identities that incorporate Taylor's formula on time scales. Moreover, we derive discrete and quantum inequalities based on these results.