AIMS Mathematics, 2020, 5(6): 7122-7144. doi: 10.3934/math.2020456.

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

1 School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, China
2 Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
3 Department of Mathematics, Faculty of Technical Science, University “Ismail Qemali”, Vlora, Albania
4 Department of mathematics, Government University, Faisalabad, Pakistan
5 Department of Mathematics, Huzhou University, Huzhou 313000, China
6 Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, P. R. China

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.
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Keywords quantum calculus; convex function; s-type convex functions; $(p_1p_2,q_1q_2)$-Ostrowski-type inequality on co-ordinates

Citation: Humaira Kalsoom, Muhammad Idrees, Artion Kashuri, Muhammad Uzair Awan, Yu-Ming Chu. Some New $(p_1p_2,q_1q_2)$-Estimates of Ostrowski-type integral inequalities via n-polynomials s-type convexity. AIMS Mathematics, 2020, 5(6): 7122-7144. doi: 10.3934/math.2020456

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