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Josip Pečarić, Anamarija Perušić and Ksenija Smoljak

Abstract

In this paper, generalizations of Steffensen’s inequality with bounds involving any two subintervals motivated by Cerone’s generalizations are given. Furthermore, weaker conditions for Cerone’s generalization as well as for new generalizations obtained in this paper are given. Moreover, functionals defined as the difference between the left-hand and the right-hand side of these generalizations are studied and new Stolarsky type means related to them are obtained.

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Neven Elezović, Josip Pečarić and Marjan Praljak

Abstract

We generalize to the n-dimensional case the set of sufficient conditions on the kernel under which the maximum principle and the potential inequality hold, given by Rao and Šikić in the 1-dimensional case. These conditions are satisfied for Hilbert-type kernels and we are able to construct new families of exponentially convex functions.

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Asif R. Khan, Josip Pečarić and Marjan Praljak

Abstract

Extension of Montgomery's identity is used in derivation of Popoviciu-type inequalities containing sums , where f is an n-convex function. Integral analogues and some related results for n-convex functions at a point are also given, as well as Ostrowski-type bounds for the integral remainders of identities associated with the obtained inequalities.

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Neda Lovričević, Josip Pečarić and Mario Krnić

Abstract

In this paper we consider Jessen's functional, defined by means of a positive isotonic linear functional, and investigate its properties. Derived results are then applied to weighted generalized power means, which yields extensions of some recent results, known from the literature. In particular, we obtain the whole series of refinements and converses of numerous classical inequalities such as the arithmetic-geometric mean inequality, Young's inequality and Hölder's inequality

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Josip Pečarić, Anamarija Perušić Pribanić and Ksenija Smoljak Kalamir

Abstract

Using Euler-type identities some new generalizations of Steffensen’s inequality for n–convex functions are obtained. Moreover, the Ostrowski-type inequalities related to obtained generalizations are given. Furthermore, using inequalities for the Čebyšev functional in terms of the first derivative some new bounds for the remainder in identities related to generalizations of Steffensen’s inequality are proven.

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Sajid Iqbal, Josip Pečarić, Muhammad Samraiz and Živorad Tomovski

Abstract

The aim of this research paper is to establish the Hardy-type inequalities for Hilfer fractional derivative and generalized fractional integral involving Mittag-Leffler function in its kernel using convex and increasing functions.