Ostrowski Type Research Articles

A Comparison and Error Analysis of Error Bounds

In this paper, we present an error analysis with the help of Ostrowski type inequalities for n-times differentiable mappings by using n-times peano kernel. A comparison is also presented which shows that obtained error bounds are better than the previous error bounds.

Majorization Inequalities via Peano's Representation of Hermite's Polynomial

The Peano's representation of Hermite polynomial and new Green functions are used to construct the identities related to the generalization of majorization type inequalities in discrete as well as continuous case. $\check{C}$eby$\check{s}$ev functional is used to find the bounds for new generalized identities and to develop the Gr$\ddot{u}$ss and Ostrowski type inequalities. Further more, we present exponential convexity together with Cauchy means for linear functionals associated with the obtained inequalities and give some applications.

Generalized Riemann-Liouville $k$ -Fractional Integrals Associated With Ostrowski Type Inequalities and Error Bounds of Hadamard Inequalities

Ostrowski inequality provides the estimation of a function to its integral mean. It is useful in error estimations of quadrature rules in numerical analysis. The objective of this paper is to define a more general form of Riemann–Liouville $k$ -fractional integrals with respect to an increasing function, which are used to obtain fractional integral inequalities of Ostrowski type. A simple and straightforward approach is followed to establish these inequalities. The applications of established results are also briefly discussed and succeeded to get bounds of some fractional Hadamard inequalities.

A parameter-based Ostrowski type inequality on time scales with k points for functions having bounded second derivatives

A parameter-based Ostrowski type inequality on time scales with k points for functions having bounded second derivatives

Uncertain fuzzy Ostrowski type inequalities for the generalized (s,m)-preinvex Godunova-Levin functions of second kind

In the present paper, the notion of the generalized (s, m)- preinvex Godunova-Levin function of second kind is introduced and some uncertain fuzzy Ostrowski type inequalities for the generalized (s, m)-preinvex Godunova-Levin functions of second kind via classical integrals and Riemann-Liouville fractional integrals are established.

Ostrowski type fractional integral inequalities for s -Godunova-Levin functions via k -fractional integrals

In this paper, we give some fractional integral inequalities of Ostrowski type for s-Godunova-Levin functions via Riemann-Liouville k- fractional integrals. We deduce some known Ostrowski type fractional integral inequalities for Riemann-Liouville fractional integrals and we also prove results for p-functions and Godunova-Levin functions by taking s=0 ans s=1 respectively.

New conformable fractional integrals of Ostrowski type using new generalized (s, m, ϕ)-preinvex mappings

AbstractIn the present paper, the notion of new generalized (s, m, ϕ)-preinvex mapping is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving new generalized (s, m, ϕ)-preinvex mappings along with beta function are given. Moreover, some generalizations of Ostrowski type inequalities for new generalized (s, m, ϕ)-preinvex mappings via conformable fractional integrals are established. At the end, some applications to special means are given.

Some new Ostrowski type fractional integral inequalities for generalized $(r;g,s,m,varphi)$-preinvex functions via Caputo $k$-fractional derivatives

In the present paper, the notion of generalized $(r;g,s,m,varphi)$-preinvex function is applied to establish some new generalizations of Ostrowski type integral inequalities via Caputo $k$-fractional derivatives. At the end, some applications to special means are given.

Certain Hermite–Hadamard type inequalities involving generalized fractional integral operators

Raina (East Asian Math J 21(2):191–203, 2005) introduced a new fractional integral operator which is a generalization of Riemann–Liouville fractional integral. Agarwal et al. (Fasc Math 204:5–27, 2016) provided some Ostrowski type fractional integral inequalities. Chen (J Math Inequal 10(1):75–81, 2016) gave extension and refinement of the Hermite–Hadamard inequality for convex functions via Riemann–Liouville fractional integrals. Here, motivated by the above-mentioned works, we aim at establishing extension and refinement of the Hermite–Hadamard type inequalities for a function with certain conditions by using new fractional integral operators introduced by Raina and Agarwal et al. above. The inequalities presented here are also pointed out to include some known results, as their special cases.

On Generalization of Dragomir’s Inequalities

In this paper, we establish some generalization of weighted Ostrowski type integral inequalities for functions of bounded variation.

Ostrowski and Simpson Type Inequalities for Strongly Reciprocally Convex Functions

Ostrowski and Simpson Type Inequalities for Strongly Reciprocally Convex Functions

Ostrowski type inequalities for sets and functions of bounded variation

In this paper we obtain sharp Ostrowski type inequalities for multidimensional sets of bounded variation and multivariate functions of bounded variation.

Some generalized Ostrowski type inequalities for functions whose second derivatives absolute values are convex and applications

We first establish some Ostrowski type inequalities for mappings whose second derivatives absolute values are convex. Then we give some special cases of these inequalities which provide extensions of those given in earlier works. Finally, some applications of these inequalities for special means are also provided.

New generalizations of Popoviciu type inequalities via new green functions and Fink’s identity

We formulate new identities involving new Green functions. Inequality of Popoviciu, which was improved by Vasić and Stanković (1976), is generalized by using newly introduced Green functions. We utilize Fink’s identity along with new Green’s function to generalize the known Popoviciu’s inequality from convex functions to higher order convex functions. Then we construct linear functionals from the generalized identities and formulate the monotonicity of these functionals utilizing the recent theory of inequalities for n-convex functions at a point. New upper bounds of Grüss and Ostrowski type are computed.

New generalizations of Popoviciu-type inequalities via new Green\u2019s functions and Montgomery identity

The inequality of Popoviciu, which was improved by Vasić and Stanković (Math. Balk. 6:281-288, 1976), is generalized by using new identities involving new Green’s functions. New generalizations of an improved Popoviciu inequality are obtained by using generalized Montgomery identity along with new Green’s functions. As an application, we formulate the monotonicity of linear functionals constructed from the generalized identities, utilizing the recent theory of inequalities for n-convex functions at a point. New upper bounds of Grüss and Ostrowski type are also computed.

A companion of Ostrowski type inequalities for mappings of bounded variation and some applications

In this paper, we establish a companion of Ostrowski type inequalities for mappings of bounded variation and the quadrature formula is also provided.

Generalizations of Hermite-Hadamard and Ostrowski type inequalities for MTm-preinvex functions

In the present paper, the notion of MTm-preinvex function is introduced and some new integral inequalities involving MTm-preinvex functions along with beta function are given. Moreover, some generalizations of Hermite-Hadamard and Ostrowski type inequalities for MTm-preinvexfunctions via classical integrals and Riemann-Liouville fractional integrals are established. These results not only extends the results appeared in the literature (see [10], [11], [12]), but also provide new estimates on these types.

Some New Ostrowski type inequalities on time scales for functions of two independent variables

By making use of the kernel given in [11], some new Ostrowski-type inequalities on time scales for double integrals are established. The results obtained here can be used in the estimation of the error.

Improvement in companion of Ostrowski type inequalities for mappings whose first derivatives are of bounded variation and applications

The main aim of this paper is to obtain a improved and generalized version of companion of Ostrowski type integral inequalities for mappings whose first derivatives are of bounded variation. Some previous results are also recaptured as special cases. New quadrature formulae are also provided.

New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion

In this paper, we have been introduced and tested some significant new bounds of Ostrowski type integral inequalities. In accordance with this purpose we have taken advantageous of the Taylor expansion for functions. Some numerical experiments have been given to show the applicability and accuracy of the proposed method.