Some New $(p_1p_2,q_1q_2)$-Estimates of Ostrowski-type integral inequalities via <i>n</i>-polynomials <i>s</i>-type convexity

Abstract

The purpose of this paper is to establish new generalization of Ostrowski type integral inequalities by using $(p, q)$-analogues which are related to the estimates of upper bound for a class of $(p_1p_2, q_1q_2)$-differentiable functions on co-ordinates. We first establish an integral identity for $(p_1p_2, q_1q_2)$-differentiable functions on co-ordinates. The result is then used to derive some estimates of upper bound for the functions whose twice partial $(p_1p_2, q_1q_2)$-differentiable functions are $n$-polynomial $s$-type convex functions on co-ordinates. Some new special cases from the main results are obtained and some known results are recaptured as well. At the end, an application to special means is given as well.