Work

Some New Bullen-Type Inequalities Obtained via Fractional Integral Operators

Year: 2023

Type: article

Abstract: In this paper, we establish a new auxiliary identity of the Bullen type for twice-differentiable functions in terms of fractional integral operators. Based on this new identity, some generalized Bullen-type inequalities are obtained by employing convexity properties. Concrete examples are given to illustrate the results, and the correctness is confirmed by graphical analysis. An analysis is provided on the estimations of bounds. According to calculations, improved Hölder and power mean inequalities give better upper-bound results than classical inequalities. Lastly, some applications to quadrature rules, modified Bessel functions and digamma functions are provided as well.

Source: Axioms

DOI: 10.3390/axioms12070691

Authors: Asfand Fahad, Saad Ihsaan Butt, Bahtiyar Bayraktar, Mehran Anwar, Yuanheng Wang

Institutions: Bahauddin Zakariya University, Zhejiang Normal University, COMSATS University Islamabad, COMSATS University Islamabad, Lahore Campus, Bursa Uludağ Üni̇versi̇tesi̇

Language: English

Topic: Mathematical Inequalities and Applications

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,779

Funders: National Natural Science Foundation of China, Zhejiang Normal University