Simpson- and Newton-Type Inequalities for Convex Functions via ( p, q )-Calculus

Waewta Luangboon, Kamsing Nonlaopon, Jessada Tariboon and Sotiris K. Ntouyas
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Waewta Luangboon: Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
Kamsing Nonlaopon: Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
Jessada Tariboon: Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
Sotiris K. Ntouyas: Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece

Mathematics, 2021, vol. 9, issue 12, 1-21

Abstract: In this paper, we establish several new ( p , q ) -integral identities involving ( p , q ) -integrals by using the definition of a ( p , q ) -derivative. These results are then used to derive ( p , q ) -integral Simpson- and Newton-type inequalities involving convex functions. Moreover, some examples are given to illustrate the investigated results.

Keywords: Simpson inequality; Newton inequality; convex function; ( p , q )-derivative; ( p , q )-integral; ( p , q )-calculus (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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