SOME BULLEN-TYPE INEQUALITIES FOR GENERALIZED FRACTIONAL INTEGRALS

Dafang Zhao, Muhammad Aamir Ali, HÃœSEYIN Budak and Zai-Yin He
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Dafang Zhao: School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, P. R. China2Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou 730000, P. R. China
Muhammad Aamir Ali: Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, P. R. China
HÜSEYIN Budak: Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey
Zai-Yin He: Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China

FRACTALS (fractals), 2023, vol. 31, issue 04, 1-11

Abstract: In this paper, we establish some new Bullen-type inequalities for differentiable convex functions using the generalized fractional integrals. The main advantage of the inequalities and operators used to obtain them is that these inequalities can be turned into some existing inequalities for Riemann integrals and new inequalities for Riemann–Liouville fractional integral inequalities and k-fractional integrals. Finally, we add some applications of special means of real numbers using the newly established inequalities to make these results more interesting.

Keywords: Midpoint Inequalities; Trapezoid Inequalities; Fractional Calculus; Convex Functions (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400601

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