A modified class of Ostrowski-type inequalities and error bounds of Hermite–Hadamard inequalities

Journal of Inequalities and Applications

Research

Sajid Iqbal¹  Muzammil Mukhtar²  Muhammad Samraiz³  Aman Ullah³  Miguel Vivas-Cortez⁴ 

[1] Department of Mathematics and Statistics, Institute of Southern Punjab, Bosan Road, Multan, Pakistan;Department of Mathematics, The Islamia University of Bahawalpur, Bahawalnagar, Pakistan;Department of Mathematics, University of Sargodha, 40100, Sargodha, Pakistan;Pontificia Universidad Católica del Ecuador, Quito, Ecuador;

关键词: Östrowski inequality;    Error estimates;    Hermite-type inequalities;    Weighted generalized Reimann–Liouville fractional integrals;    26D15;    26A51;    26A33;    05A30;   

DOI  :  10.1186/s13660-023-03035-8

 received in 2023-05-20, accepted in 2023-09-18,  发布年份 2023

来源: Springer

【 摘 要 】

This paper aims to extend the application of the Ostrowski inequality, a crucial tool for figuring out the error bounds of various numerical quadrature rules, including Simpson’s, trapezoidal, and midpoint rules. Specifically, we develop a more comprehensive class of Ostrowski-type inequalities by utilizing the weighted version of Riemann–Liouville (RL) fractional integrals on an increasing function. We apply our findings to estimate the error bounds of Hadamard-type inequalities. Our results are more comprehensive, since we obtain the results of the existing literatures as particular cases for certain parameter values. This research motivates researchers to apply this concept to other fractional operators.

【 授权许可】

CC BY   
© Springer Nature Switzerland AG 2023

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