FRACTIONAL VERSIONS OF OSTROWSKI AND RELATED INEQUALITIES WITH APPLICATIONS

Weidong Zhao, Ghulam Farid, Jongsuk Ro, Atiq Rehman and Ibrahim Mekawy
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Weidong Zhao: School of Computer Science, Chengdu University, Chengdu 610106, P. R. China
Ghulam Farid: ��Department of Mathematics, COMSATS University Islamabad, Attock 43600, Pakistan
Jongsuk Ro: ��School of Electrical and Electronics Engineering, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea§Department of Intelligent Energy and Industry, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea
Ibrahim Mekawy: �Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 08, 1-10

Abstract: The inequality Ψ(σ) − 1 u2 − u1∫u1u2Ψ(λ)dλ ≤ 1 4 + (σ −u1+u2 2 )2 (u2 − u1)2 (u2 − u1)ℳ, is well known in literature as Ostrowski inequality. This paper aims to find two fractional versions of this inequality by utilizing definitions of Riemann–Liouville fractional integrals. By applying these inequalities on some fixed points, error bounds of fractional Hermite–Hadamard inequalities are obtained. Further, an Ostrowski–Grüss type inequality is also proved.

Keywords: Ostrowski Inequality; Hermite–Hadamard Inequality; Grüss Inequality; Riemann–Liouville Fractional Integrals; Symmetric Function (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25400936

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