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

Humaira Kalsoom; Muhammad Idrees; Artion Kashuri; Muhammad Uzair Awan; Yu-Ming Chu; Humaira Kalsoom; Muhammad Idrees; Artion Kashuri; Muhammad Uzair Awan; Yu-Ming Chu

doi:10.3934/math.2020456

AIMS Mathematics

2020, Volume 5, Issue 6: 7122-7144. doi: 10.3934/math.2020456

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Research article

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

Received: 14 July 2020 Accepted: 24 August 2020 Published: 10 September 2020
MSC : 26A51, 26A33, 26D07, 26D10, 26D15

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

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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.

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