HERMITE–HADAMARD TYPE INTEGRAL INEQUALITIES INVOLVING FRACTIONAL INTEGRALS FOR THE s–CONVEX FUNCTIONS IN THE FOURTH SENSE

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Tınaztepe G., Eken Z., Kemali S., Sezer Evcan S., Sezer S.

JOURNAL OF MATHEMATICAL INEQUALITIES, cilt.19, sa.3, ss.765-778, 2025 (SCI-Expanded)

Özet

In this paper, the Hermite-Hadamard type inequalities involving Riemann-Liouville fractional integrals for s-convex functions in the fourth sense are obtained. By means of certain integral identities for fractional integrals, some inequality relations among fractional integrals of the fourth sense s-convex functions and the functions whose derivatives are s-convex in the fourth sense are set forth. Moreover, based on the obtained results, some inequality relations among special functions including beta, incomplete beta functions, and means including logarithmic and arithmetic mean are given as applications.