NEWTON-TYPE INEQUALITIES ASSOCIATED WITH CONVEX FUNCTIONS VIA QUANTUM CALCULUS

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Luangboon W., Nonlaopon K., Sarikaya M. Z., Budak H.

MISKOLC MATHEMATICAL NOTES, vol.25, no.1, pp.383-398, 2024 (SCI-Expanded, Scopus)

• Publication Type: Article / Article
• Volume: 25 Issue: 1
• Publication Date: 2024
• Doi Number: 10.18514/mmn.2024.4203
• Journal Name: MISKOLC MATHEMATICAL NOTES
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
• Page Numbers: pp.383-398
• Open Archive Collection: AVESIS Open Access Collection
• Kocaeli University Affiliated: No

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.