Ostrowski Type Research Articles

On some new Hermite-Hadamard and Ostrowski type inequalities for s-convex functions in (p, q)-calculus with applications

Abstract In this study, we establish some new Hermite-Hadamard type inequalities for s-convex functions in the second sense using the post-quantum calculus. Moreover, we prove a new ( p , q ) \left(p,q) -integral identity to prove some new Ostrowski type inequalities for ( p , q ) \left(p,q) -differentiable functions. We also show that the newly discovered results are generalizations of comparable results in the literature. Finally, we give application to special means of real numbers using the newly proved inequalities.

New Ostrowski type inequalities pertaining to conformable fractional operators

The advancements of integral inequalities with the help of fractional operators have recently been the focus of attention in the theory of inequalities. In this study, we first review some fundamental concepts, and then using \(k\)-conformable fractional integrals, we establish a new integral identity for differentiable functions. Then, considering this identity as an auxiliary result, several Ostrowski-type inequalities are presented for functions whose modulus of the first derivatives are quasi-convex. The obtained results represent generalizations as well as refinements for some published results.

General form of $(\lambda,\varphi)$-additive operators on spaces of $L$-space-valued functions

The goal of the article is to characterize continuous $(\lambda,\varphi)$-additive operators acting on measurable bounded functions with values in $L$-spaces. As an application, we prove a sharp Ostrowski type inequality for such operators.

Improvement of Some Hayashi–Ostrowski Type Inequalities with Applications in a Probability Setting

Different types of mathematical inequalities have been largely analyzed and employed. In this paper, we introduce improvements to some Ostrowski type inequalities and present their corresponding proofs. The presented proofs are based on applying the celebrated Hayashi inequality to certain functions. We provide examples that show these improvements. Illustrations of the obtained results are stated in a probability framework.

A novel analysis of integral inequalities in the frame of fractional calculus

In this paper, we define and explore the new family of exponentially convex functions which are called exponentially s–convex functions. We attain the amazing examples and algebraic properties of this newly introduced function. In addition, we find a novel version of Hermite-Hadamard type inequality in the support of this newly introduced concept via the frame of classical and fractional calculus (non-conformable and Riemann-Liouville integrals operator). Furthermore, we investigate refinement of Hermite-Hadamard type inequality by using exponentially s–convex functions via fractional integraloperator. Finally, we elaborate some Ostrowski type inequalities in the frame of fractional calculus. These new results yield us some generalizations of the prior results.

Fuzzy Ostrowski type inequalities via ϕ - λ -convex functions

We would like to state well-known Ostrowski inequality via \(\phi\)-\(\lambda\)-convex by using the Fuzzy Reimann integrals. In addition, we establish some Fuzzy Ostrowski type inequalities for the class of functions whose derivatives in absolute values at certain powers are \(\phi\)-\(\lambda\)-convex by Holder's and power mean inequalities. We are introducing very first time that the class of \(\phi\)-\(\lambda\)-convex function, which is the generalization of many important classes including class of \(h\)-convex, Godunova-Levin \(s\)-convex, \(s\)-convex in the \(2^{\rm nd}\) kind and hence contains convex functions. It also contains class of \(P\)-convex and class of Godunova-Levin. In this way we also capture the results with respect to convexity of functions.

General Opial Type Inequality and New Green Functions

In this paper we provide many new results involving Opial type inequalities. We consider two functions—one is convex and the other is concave—and prove a new general inequality on a measure space (Ω,Σ,μ). We give an new result involving four new Green functions. Our results include Grüss and Ostrowski type inequalities related to the generalized Opial type inequality. The obtained inequalities are of Opial type because the integrals contain the function and its integral representation. They are not a direct generalization of the Opial inequality.

New Fractional Mercer–Ostrowski Type Inequalities with Respect to Monotone Function

This research focuses on Ostrowski type inequality in the form of classical Mercer inequality viaψ-Riemann–Liouville fractional integral (F-I) operators. Using theψ-Riemann–Liouville F-I operator, we first develop and demonstrate a new generalized lemma for differentiable functions. Based on this lemma, we derive some fractional Mercer–Ostrowski type inequalities by using the convexity theory. These new findings extend and recapture previous published results. Finally, we presented applications of our work via the known special functions of real numbers such as q-digamma functions and Bessel function.

Some Inequalities of Ostrowski Type for Double Integral Mean of Absolutely Continuous Functions

In this paper we establish some Ostrowski type inequalities for double integral mean of absolutely continuous functions. An application for special means is given as well.

Some new generalized Ostrowski type inequalities with new error bounds

In this paper, we will ameliorate and generalize Ostrowski type inequality for twice differentiable mappings in various Lebesgue spaces. Some famous inequalities can be derived as a special cases of the inequalities obtained here. Furthermore, perturbed mid-point inequality and perturbed trapezoid inequality are also obtained. The obtained inequalities have very rapid applications in numerical integrations and some special means.

Some Perturbed Inequalities of Ostrowski Type for Functions whose n-th Derivatives Are Bounded

We firstly establish an identity for $n$ time differentiable mappings Then, a new inequality for $n$ times differentiable functions is deduced. Finally, some perturbed Ostrowski type inequalities for functions whose $n$th derivatives are of bounded variation are obtained.

On approximation of hypersingular integral operators by bounded ones

We solve the Stechkin problem about the approximation of generally speaking unbounded hypersingular integral operators by bounded ones. As a part of the proof, we also solve several related and interesting on their own problems. In particular, we obtain sharp Landau-Kolmogorov type inequalities in both additive and multiplicative forms for hypersingular integral operators and prove a sharp Ostrowski type inequality for multivariate Sobolev classes. We also give some applications of the obtained results, in particular, study the modulus of continuity of the hypersingular integral operators, and solve the problem of optimal recovery of the value of a hypersingular integral operator based on the argument known with an error.

On Ostrowski Type Inequalities via the Extended Version of Montgomery’s Identity

In this paper, we obtain new Ostrowski type inequalities by using the extended version of Montgomery identity and Green’s functions. We also give estimations of the difference between two integral means.

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.

Ostrowski Type Inequalities for s -Convex Functions via q -Integrals

The new outcomes of the present paper are q -analogues ( q stands for quantum calculus) of Hermite-Hadamard type inequality, Montgomery identity, and Ostrowski type inequalities for s -convex mappings. Some new bounds of Ostrowski type functionals are obtained by using Hölder, Minkowski, and power mean inequalities via quantum calculus. Special cases of new results include existing results from the literature.

A New Companion Inequality of Ostrowski's type with Applications to P.D.F.'s

In this paper, variant inequalities of Ostrowski’s type for absolutely continuous mappings whose derivatives are monotonic, belongs to L1[a, b], Lq[a, b], (q > 1) and L∞[a, b] are established.

Weighted Ostrowski type inequalities for co-ordinated convex functions

In this paper, utilizing an identity given by Yıldız and Sarıkaya in (Yildiz and Sarikaya in Int. J. Anal. Appl. 13(1):64–69, 2017), we establish some weighted Ostrowski type inequalities for co-ordinated convex functions in a rectangle from the plane mathbb{R} ^{2}. Moreover, as special cases of our main results, we give some weighted Hermite–Hadamard type inequalities. The results given in this paper provide generalizations of some result established in earlier works.

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>

Ostrowski type inequalities for exponentially s-convex functions on time scale

<abstract><p>In this paper we establish some new inequalities of Ostrowski type for exponentially s-convex functions and s-convex functions on time scale. We also make comparison of our new results with already existing results by imposing some conditions.</p></abstract>

Fractional Ostrowski type inequalities for differentiable harmonically convex functions

<abstract><p>In this paper, we prove some new Ostrowski type inequalities for differentiable harmonically convex functions using generalized fractional integrals. Since we are using generalized fractional integrals to establish these inequalities, therefore we obtain some new inequalities of Ostrowski type for Riemann-Liouville fractional integrals and $ k $-Riemann-Liouville fractional integrals in special cases. Finally, we give some applications to special means of real numbers for newly established inequalities.</p></abstract>