New Inequalities of Bullen-type for Twice-Differentiable Functions via Conformable Fractional Integrals

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Hezenci F., BUDAK H.

International Journal of Applied and Computational Mathematics, cilt.10, sa.6, 2024 (Scopus)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 10 Sayı: 6
• Basım Tarihi: 2024
• Doi Numarası: 10.1007/s40819-024-01804-7
• Dergi Adı: International Journal of Applied and Computational Mathematics
• Derginin Tarandığı İndeksler: Scopus
• Anahtar Kelimeler: 26A33, 26D07, 26D10, Bullen-type inequalities, Conformable fractional integrals, Convex functions, Riemann–Liouville fractional integrals
• Kocaeli Üniversitesi Adresli: Evet

Özet

In this paper, an equality for the case of twice-differentiable convex functions is established by the conformable fractional integrals. In addition, sundry Bullen-type inequalities are acquired by conformable fractional integrals for the case of twice-differentiable functions. Moreover, several Bullen-type inequalities are obtained by taking advantage of the convexity, the Hölder inequality, and the power mean inequality. Finally, we derive our important results by using special cases of obtained theorems. In future studies, the ideas and strategies for our results related Bullen-type inequalities by conformable fractional integrals may open new ways for mathematicians in this area.