Ostrowski Type Inequalities Research Articles

Opial and Ostrowski type inequalities based on trigonometric and hyperbolic type Taylor formulae

Based on [4], we produce a collection of interesting trigonometric and hyperbolic Taylor formulae with integral remainders. Using these we derive Opial and Ostrowski type corresponding inequalities of various kinds and norms.

A Note on the New Ostrowski and Hadamard Type Inequalities via the Hölder–İşcan Inequality

For all convex functions, the Hermite–Hadamard inequality is already well known in convex analysis. In this regard, Hermite–Hadamard and Ostrowski type inequalities were obtained using exponential type convex functions in this work. In addition, new generalizations were found for different values of θ. In conclusion, we believe that our work’s technique will inspire more study in this field.

On the Generalization of Ostrowski-Type Integral Inequalities via Fractional Integral Operators with Application to Error Bounds

The Ostrowski inequality expresses bounds on the deviation of a function from its integral mean. The Ostrowski’s type inequality is frequently used to investigate errors in numerical quadrature rules and computations. In this work, Ostrowski-type inequality is demonstrated using the generalized fractional integral operators. From an application perspective, we present the bounds of the fractional Hadamard inequalities. The results that are being presented involve a number of fractional inequalities that are already known and have been published.

Korneichuk-Stechkin Lemma, Ostrowski and Landau Inequalities, and Optimal Recovery Problems for L-Space Valued Functions

We prove an analogue of the Korneichuk–Stechkin lemma for functions with values in L-spaces. As applications, we obtain sharp Ostrowski type inequalities and solve problems of optimal recovery of identity and convexifying operators, as well as the problem of integral recovery on the classes of L-space valued functions with given majorant of modulus of continuity. The recovery is done based on n mean values of the functions over intervals. Moreover, on the classes of functions with given majorant of modulus of continuity of their Hukuhara type derivative, we solve the problem of optimal recovery of the function and the Hukuhara type derivative. The recovery is done based on n values of the function. We obtain sharp Landau type inequalities and solve an analogue of the Stechkin problem about approximation of unbounded operators by bounded ones and the problem of optimal recovery of an unbounded operator on a class of elements, known with error. Consideration of L-space valued functions gives a unified approach to solution of the mentioned above extremal problems for the classes of multi- and fuzzy-valued functions, and for the classes of functions with values in Banach spaces, in particular random processes, and many other classes of functions.

K-fractional Ostrowski type inequalities via (s, r)-conex

We are introducing very first time a generalized class named it the class of (s, r)-convex in mixed kind, this class includes s-convex in 1st and 2nd kind, P-convex, quasi-convex, and the class of ordinary convex. Also, we would like to state the generalization of the classical Ostrowski inequality via k-fractional integrals, which is obtained for functions whose first derivative in absolute values is (s, r)-convex in mixed kind. Moreover, we establish some Ostrowski type inequalities via k-fractional integrals and their particular cases for the class of functions whose absolute values at certain powers of derivatives are (s, r)-convex in mixed kind by using different techniques including Holder's inequality and power mean inequality. Also, various established results would be captured as special cases. Moreover, some applications in terms of special means would also be given.

Generalization of Steffensen's inequality for higher order convex function involving extensions of montgomery identities on time scales

ABSTRACT Generalizations of some Steffensen's inequalities for the class of higher order convex functions are obtained in present study. To prove the results, some preliminary lemmas are established by using extended Montgomery identities via Taylor's formula on time scales. Furthermore, Ostrowski type inequalities are also established, along with prove of optimization of the constant. Moreover, newly obtained results are discussed in discrete and quantum calculus as well.

Some q-Symmetric Integral Inequalities Involving s-Convex Functions

The q-symmetric analogues of Hölder, Minkowski, and power mean inequalities are presented in this paper. The obtained inequalities along with a Montgomery identity involving q-symmetric integrals are used to extend some Ostrowski-type inequalities. The q-symmetric derivatives of the functions involved in these Ostrowski-type inequalities are convex or s-convex. Moreover, some Hermite–Hadamard inequalities for convex functions as well as for s-convex functions are also acquired with the help of q-symmetric calculus in the present work. Some examples are included to support the effectiveness of the proved results.

Generalizations of Hardy-Type Inequalities by Montgomery Identity and New Green Functions

In this paper we extend general Hardy’s inequality by appropriately combining Montgomery’s identity and Green functions. Related Grüss and Ostrowski-type inequalities are also derived.

Some New Hermite-Hadamard and Ostrowski Type Inequalities for s-Preinvex Functions in (p,q)-Calculus With Applications

Some New Hermite-Hadamard and Ostrowski Type Inequalities for s-Preinvex Functions in (p,q)-Calculus With Applications

Study of quantum Ostrowski's-type inequalities for differentiable convex functions

UDC 517.9 We prove some new q-Ostrowski's-type inequalities for differentiable and bounded functions. Moreover, we present the relationship between the newly established and already known inequalities, which is very interesting for new readers. Some applications to special means of real numbers are given to make the results more valuable.

Ostrowski Type Inequalities via Some Exponentially s-Preinvex Functions on Time Scales with Applications

Integral inequalities concerned with convexity have many applications in several fields of mathematics in which symmetry plays an important role. In the theory of convexity, there exist strong connections between convexity and symmetry. If we are working on one of the concepts, then it can be applied to the other of them. In this paper, we establish some novel generalizations of Ostrowski type inequalities for exponentially s-preinvex and s-preinvex functions on time scale by using Hölder inequality and Montgomery Identity. We also obtain applications to some special means. These results are motivated by the symmetric results obtained in the recent article by Abbasi and Anwar in 2022 on Ostrowski type inequalities for exponentially s-convex functions and s-convex functions on time scale. Moreover, we discuss several special cases of the results obtained in this paper.

On Ostrowski-type inequalities via Fink identity

In this paper, we use the well-known classical Fink identity and some new and previously defined Green’s functions to derive new Ostrowski-type inequalities. For this purpose, we use some identities which are defined under the conditions of sum and integral. We also estimate the difference between the two integral means.

Fractional version of Ostrowski-type inequalities for strongly p-convex stochastic processes via a k-fractional Hilfer–Katugampola derivative

In the present research, we introduce the notion of convex stochastic processes namely; strongly p-convex stochastic processes. We establish a generalized version of Ostrowski-type integral inequalities for strongly p-convex stochastic processes in the setting of a generalized k-fractional Hilfer–Katugampola derivative by using the Hölder and power-mean inequalities. By using our main results, we derived some known results as special cases and many well-known existing results are also recaptured. It is assumed that this research will offer new guidelines in fractional calculus.

FRACTIONAL OSTROWSKI TYPE INEQUALITIES FOR (s,m)-CONVEX FUNCTION WITH APPLICATIONS

In this paper, we introduce [Formula: see text]-convex function, and obtain a new identity by the method called integrating by parts. Based on the identity, many Ostrowski type inequalities are presented through the Hölder’s inequality and the well-known power-mean inequality. Under certain conditions, the results we obtained can be transformed into the classical results. Of course, at the end of the paper, some examples are given to support the main results.

Generalisation of Ostrowski's type inequalities by using multi-step quadratic kernel

Generalisation of Ostrowski's type inequalities by using multi-step quadratic kernel

On certain Ostrowski type integral inequalities for convex function via AB-fractional integral operator

<abstract><p>We investigate and prove a new lemma for twice differentiable functions with the fractional integral operator $ AB $. Based on this newly developed lemma, we derive some new results about this identity. These new findings provide some generalizations of previous findings. This research builds on a novel new auxiliary result that allows us to create new variants of Ostrowski type inequalities for twice differentiable convex mappings. Some of the newly presented results' special cases are also discussed. As applications, several estimates involving special means of real numbers and Bessel functions are depicted.</p></abstract>

Ostrowski type inequalities for functions of two variables via generalized fractional integrals

Ostrowski type inequalities for functions of two variables via generalized fractional integrals

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.

Some weighted Hadamard and Ostrowski-type fractional inequalities for quasi-geometrically convex functions

It is well knowledge that the purpose of inequality is to develop various approaches to mathematical problem solving. In order to prove the originality and existence of mathematical techniques, it is now necessary to seek exact inequalities. In the present research, we propose some novel weighted fractional Ostrowski-type inequalities for functions which are differentiable and satisfy quasi-geometrically convex using a new identity. Moreover, outcomes for functions with a bounded first derivative are proved. Finally, some examples are given to illustrate the investigated results. The obtained results generalize and refine previously known results.

Ostrowski type inequalities via exponentially $s$-convexity on time scales

We introduce the concept of exponentially $s$-convexity in the second sense on a time scale interval. We prove among other things that if $f: [a, b]\to \mathbb{R}$ is an exponentially $s$-convex function, then \begin{align*} &\frac{1}{b-a}\int_a^b f(t)\Delta t\\ &\leq \frac{f(a)}{e_{\beta}(a, x_0) (b-a)^{2s}}(h_2(a, b))^s+\frac{f(b)}{e_{\beta}(b, x_0) (b-a)^{2s}}(h_2(b, a))^s, \end{align*} where $\beta$ is a positively regressive function. By considering special cases of our time scale, one can derive loads of interesting new inequalities. The results obtained herein are novel to best of our knowledge and they complement existing results in the literature.