Newton-type inequalities associated with convex functions via quantum calculus

Luangboon, Waewta and Nonlaopon, Kamsing and Sarikaya, Mehmet Zeki and Budak, Hüseyin (2024) Newton-type inequalities associated with convex functions via quantum calculus. Miskolc Mathematical Notes, 25 (1). pp. 383-398. ISSN 1787-2413

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Abstract

In this paper, we firstly establish an identity by using the notions of quantum derivatives and integrals. Using this quantum identity, quantum Newton-type inequalities associated with convex functions are proved. We also show that the newly established inequalities can be recaptured into some existing inequalities by taking q → 1−. Finally, we give mathematical examples of convex functions to verify the newly established inequalities.

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