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

• Published in: AIMS mathematics Vol. 5; no. 6; pp. 7122 - 7144
• Main Authors: Kalsoom, Humaira, Idrees, Muhammad, Kashuri, Artion, Uzair Awan, Muhammad, Chu, Yu-Ming
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2020
• Subjects: convex function; p_1p_2; q_1q_2)$-ostrowski-type inequality on co-ordinates; quantum calculus; s-type convex functions
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2020456

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.