Ostrowski Type Integral Inequalities Research Articles

Some new results of ostrowski type inequalities using 4-step quadratic kernel and their applications

This work is a generalization of Ostrowski type integral inequalities using a special 4-step quadratic kernel. Some new and useful results are obtained. Applications to Quadrature Rules and special Probability distribution are also evaluated.

Post-Quantum Integral Inequalities for Three-Times (p,q)-Differentiable Functions

A new (p,q)-integral identity involving left and right post quantum derivatives, by using three times (p,q)-differentiable functions is established and then this identity is used to derive several new post-quantum Ostrowski type integral inequalities for three times (p,q)-differentiable functions. These results are generalizations of corresponding results in the area of integral inequalities.

Integral inequalities for differentiable s-convex functions in the second sense via Atangana-Baleanu fractional integral operators

Fractional integral operators, which form strong links between fractional analysis and integral inequalities, make unique contributions to the field of inequality theory due to their properties and strong kernel structures. In this context, the novelty brought to the field by the study can be expressed as the new and first findings of Ostrowski type that contain Atangana-Baleanu fractional integral operators for differentiable s-convex functions in the second sense. In the study, two new integral identities were established for Atangana-Baleanu fractional integral operators and by using these two new integral identities, Ostrowski type integral inequalities were obtained. In the findings, it was aimed to contribute to the field due to the structural properties of Atangana-Baleanu fractional integral operators.

On the generalized Ostrowski type inequalities for co-ordinated convex functions

The purpose of this article is to establish some generalized Ostrowski type inequalities and integral inequalities in the coordinate plane for convex functions of 2 variables. For this, we will specify a generalized identity, and with the help of this integral identity, we will examine the Ostrowski, trapezoid, and midpoint type integral inequalities, including Riemann integral and Riemann-Liouville fractional integral. In this way, we aim to contribute to the generalization of integral inequalities, an important topic in mathematical analysis.

Weighted Ostrowski's Type Integral Inequalities for Mapping Whose Second Derivative is Bounded

The aim of this paper is to concentrate on the domain of $L_{\infty },$ $% L_{p},$ and $L_{1}$ norms of inequalities and their applications for some special weight functions. For different weights some previous results are recaptured. Applications are also discussed.

Some New Generalized Inequalities with regard to Two-Dimensional Preinvex Functions

In this study, we investigated the general convexity of functions which is named preinvexity. Firstly, we generalized Hermite-Hadamard type integral inequality for two-dimensional preinvex functions. Then, we obtained a generalization of Ostrowski type integral inequality for two-dimensional preinvex functions. Besides, we derived some new generalized inequalities related to these functions.

Weighted Ostrowski's Type Integral Inequalities for Mapping Whose First Derivative Is Bounded

The aim of paper is to develop the inequalities for L∞, Lp and L1 norms. Applications for some special weight functions and Perturbed expressions are also determined via Chebychev functional. We recaptured the previous results for different weights.

Post-quantum Ostrowski type integral inequalities for twice (p,q)-differentiable functions

Post-quantum Ostrowski type integral inequalities for twice (p,q)-differentiable functions

Weighted Ostrowski type inequalities via Montgomery identity involving double integrals on time scales

<abstract><p>In this paper, the Montgomery identity is generalized for double integrals on time scales by employing a novel analytical approach to develop the generalized Ostrowski type integral inequalities involving double integrals. Some inimitable cases are discussed for different parameters and parametric functions. Moreover, applications to some particular time scales are also presented.</p></abstract>

Post-quantum Ostrowski type integral inequalities for functions of two variables

<abstract><p>In this study, we give the notions about some new post-quantum partial derivatives and then use these derivatives to prove an integral equality via post-quantum double integrals. We establish some new post-quantum Ostrowski type inequalities for differentiable coordinated functions using the newly established equality. We also show that the results presented in this paper are the extensions of some existing results.</p></abstract>

Ostrowski type integral inequalities, weighted Ostrowski, and trapezoid type integral inequalities with powers

In this paper, we prove some new weighted Ostrowski and Trapezoid type inequalities with powers on time scales. The results will be proved by employing the generalized version of Montgomery identity with weights on time scales designed and proved for this purpose. As special cases, we will derive some new weighted discrete inequalities of Ostrowski and Trapezoid types which to the best of the authors' knowledge are essentially new.

Refinements of Ostrowski Type Integral Inequalities Involving Atangana–Baleanu Fractional Integral Operator

In this article, first, we deduce an equality involving the Atangana–Baleanu (AB)-fractional integral operator. Next, employing this equality, we present some novel generalization of Ostrowski type inequality using the Hölder inequality, the power-mean inequality, Young’s inequality, and the Jensen integral inequality for the convexity of |Υ|. We also deduced some new special cases from the main results. There exists a solid connection between fractional operators and convexity because of their fascinating properties in the mathematical sciences. Scientific inequalities of this nature and, particularly, the methods included have applications in different fields in which symmetry plays a notable role. It is assumed that the results presented in this article will show new directions in the field of fractional calculus.

A new version of Ostrowski type integral inequalities for different differentiable mapping

In this paper, improved and generalized version of Ostrowski’s type inequalities is established. The parameters used in the peano kernels help us to obtain previous results. The obtained bounds are then applied to numerical integration.

Ostrowski-type inequalities for n-polynomial mathscr{P}-convex function for k-fractional Hilfer\u2013Katugampola derivative

In this article, we develop a novel framework to study a new class of convex functions known as n-polynomial mathscr{P} -convex functions. The purpose of this article is to establish a new generalization of Ostrowski-type integral inequalities by using a generalized k-fractional Hilfer–Katugampola derivative. We employ this technique by using the Hölder and power-mean integral inequalities. We present analogs of the Ostrowski-type integrals inequalities connected with the n-polynomial mathscr{P}-convex function. Some new exceptional cases from the main results are obtained, and some known results are recaptured. In the end, an application to special means is given as well. The article seeks to create an exciting combination of a convex function and special functions in fractional calculus. It is supposed that this investigation will provide new directions in fractional calculus.

Generalized fractional Ostrowski type integral inequalities for logarithmically h-convex function

The authors have tried to prove a fractional integral identity generalizing already some existing identities. Based on, some Ostrowski-type fractional integral inequalities for r-times differentiable functions have been discussed, generalizing some existing results in the literature. As a consequence, some new Ostrowski-type, Hermite–Hadamard type and mid point type inequalities have been derived.

Novel Refinements via n –Polynomial Harmonically s –Type Convex Functions and Application in Special Functions

In this work, we introduce the idea of n –polynomial harmonically s –type convex function. We elaborate the new introduced idea by examples and some interesting algebraic properties. As a result, new Hermite–Hadamard, some refinements of Hermite–Hadamard and Ostrowski type integral inequalities are established, which are the generalized variants of the previously known results for harmonically convex functions. Finally, we illustrate the applicability of this new investigation in special functions (hypergeometric function and special mean of real numbers).

Erratum: A companion of Ostrowski type integral inequality using a 5-step Kernel with some applications

The aim of this paper is to correct results from the published paper: A companion of Ostrowski Type Integral Inequality Using a 5-Step Kernel with Some Applications, Filomat 30:13 (2016), 3601-3614.

Some New $(p_1p_2,q_1q_2)$-Estimates of Ostrowski-type integral inequalities via <i>n</i>-polynomials <i>s</i>-type convexity

The purpose of this paper is to establish new generalization of Ostrowski type integral inequalities by using $(p, q)$-analogues which are related to the estimates of upper bound for a class of $(p_1p_2, q_1q_2)$-differentiable functions on co-ordinates. We first establish an integral identity for $(p_1p_2, q_1q_2)$-differentiable functions on co-ordinates. The result is then used to derive some estimates of upper bound for the functions whose twice partial $(p_1p_2, q_1q_2)$-differentiable functions are $n$-polynomial $s$-type convex functions on co-ordinates. Some new special cases from the main results are obtained and some known results are recaptured as well. At the end, an application to special means is given as well.

Some New Inequalities of Ostrowski Type for Double Integrals via Fractional Integral Operators

In this paper, we first obtain the useful identity for double integrals via fractional integral operators. Then with the help of this identity we outline some significant Ostrowski type integral inequalities for functions in two variables. In accordance with this purpose we benefit from the properties of bounded function and concave mappings on co-ordinates. The established results are extensions of some existing Ostrowski type inequalities in the previous published studies.

Some new Ostrowski type fractional integral inequalities for generalized relative semi-(r; m, h)-preinvex mappings via Caputo k -fractional derivatives

In the present paper, the notion of generalized relative semi-(r; m, h)-preinvex mappings is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving generalized relative semi-(r; m, h)-preinvex mappings are given.Moreover, some new generalizations of Ostrowski type integral inequalities to generalized relative semi-(r; m, h)-preinvex mappings that are (n + 1)-differentiable via Caputo k-fractional derivatives are established. Some applications to special means are also obtain. It is pointed out that some new special cases can be deduced from main results of the article.