Some New Bullen-Type Inequalities Obtained via Fractional Integral Operators

Autor:	Asfand Fahad, Saad Ihsaan Butt, Bahtiyar Bayraktar, Mehran Anwar, Yuanheng Wang
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	convex functions Bullen’s inequality Hadamard inequality Hölder inequality power mean fractional integral operators Mathematics QA1-939
Zdroj:	Axioms, Vol 12, Iss 7, p 691 (2023)
Druh dokumentu:	article
ISSN:	2075-1680
DOI:	10.3390/axioms12070691
Popis:	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.
Databáze:	Directory of Open Access Journals
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