Andrea Aglić Aljinović

Weighted Montgomery identity for the fractional integral of a function with respect to another function

Abstract. We present a weighted Montgomery identity for the fractional integral of a function f with respect to another function g and use it to obtain weighted Ostrowski type inequalities for fractional integrals involving functions whose first derivatives belong to Lp spaces. These inequalities are generally sharp in case p>1

Montgomery Identity and Ostrowski Type Inequalities for Riemann-Liouville Fractional Integral

p>1

Error bounds for weighted 2-point and 3-point Radau and Lobatto quadrature rules for functions of bounded variation

and best possible in case p=1

Generalizations of Steffensen's inequality via weighted Montgomery identity

p=1

Improvements of some Ostrowski type inequalities

. Applications for the Hadamard fractional integrals are given.

On Landau type inequalities via Ostrowski inequalities

We present Montgomery identity for Riemann-Liouville fractional integral as well as for fractional integral of a function with respect to another function . We further use them to obtain Ostrowski type inequalities involving functions whose first derivatives belong to spaces. These inequalities are generally sharp in case and the best possible in case . Application for Hadamard fractional integrals is given.

General Integral Identities and Related Inequalities

We present a weighted generalization of Montgomery identity for Riemann-Stieltjes integral and use it to obtain weighted generalization of a recently obtained inequality, as well as weighted 2-point and 3-point quadrature formulae of closed and semi-closed type for functions of bounded variation.

On weighted Euler harmonic identities with applications

Some new generalizations of Steffensens inequality are obtained by means of weighted Montgomery identity and estimations between difference of two weighted integral means. Further, functionals associated to these new generalizations are observed and used to generate n-exponentially and exponentially convex functions as well as to obtain new Stolarsky type means related to these functionals.