Some new estimates of  integral inequalities and their applications

B. Bayraktar; S. I. Butt; J. E. Nápoles; F. Rabossi

doi:10.3842/umzh.v76i2.7266

B. Bayraktar Faculty of Education, Bursa Uludag University, Gorukle Campus, Turkey
S. I. Butt COMSATS University Islamabad Lahore Campus, Pakistan
J. E. Nápoles UNNE, FaCENA, Corrientes, Argentina; UTN-FRRE, Resistencia, Chaco, Argentina
F. Rabossi UTN-FRRE, Resistencia, Chaco, Argentina

DOI: https://doi.org/10.3842/umzh.v76i2.7266

Keywords: convex function, quasi-convex, Hermite-Hadamard type inequality, Simpson type inequalities, Riemann-Liouville fraction integrals, Lipschitz condition, Lagrange theorem

Abstract

UDC 517.9, 517.928

We obtain several new integral inequalities in terms of fractional integral operators for the functions whose first derivatives satisfy either the conditions of the Lagrange theorem or the Lipschitz condition. In some special cases, the results obtained provide better upper estimates than those known in the literature for Bullen-type inequality and Hadamard-type right-hand side inequality. Finally, some error estimates for the trapezoidal formula are discussed.

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