Ostrowski Type Research Articles

Hermite-Hadamard and Ostrowski type inequalities in $ \mathfrak{h} $-calculus with applications

<abstract><p>In this paper, we prove Hermite-Hadamard inequality for convex functions in the framework of $ \mathfrak{h} $-calculus. We also use the notions of $ \mathfrak{h} $-derivative and $ \mathfrak{h} $-integral to prove Ostrowski's and trapezoidal type inequalities for bounded functions. It is also shown that the newly established inequalities are the generalization of the comparable inequalities in the literature. Finally, using some examples, we demonstrate the validity of newly formed inequalities and show how they can be used to special means of real numbers.</p></abstract>

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

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

Fuzzy Ostrowski type inequalities via h-convex

We would like to state well-known Ostrowski inequality via h-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 h-convex by Holder’s and power mean inequalities. This class of h-convex function, which is the generalization of many important classes including class of Godunova-Levin s-convex, s-convex in the 2nd 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.

On Ostrowski Type Inequalities for Generalized Integral Operators

It is well known that mathematical inequalities have played a very important role in solving both theoretical and practical problems. In this paper, we show some new results related to Ostrowski type inequalities for generalized integral operators.

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>

Generalizations of Ostrowski type inequalities via $ F $-convexity

<abstract><p>The aim of this article is to give new generalizations of both the Ostrowski's inequality and some of its new variants with the help of the $ F $-convex function class, which is a generalization of the strongly convex functions. Young's inequality, which is well known in the literature, as well as Hölder's inequality, was used to obtain the new results. Also we obtain some results for convex and strongly convex functions by utilizing these inequalities.</p></abstract>

Some Ostrowski type inequalities for mappings whose second derivatives are preinvex function via fractional integral operator

<abstract><p>The comprehension of inequalities in preinvexity is very important for studying fractional calculus and its effectiveness in many applied sciences. In this article, we develop and study of fractional integral inequalities whose second derivatives are preinvex functions. We investigate and prove new lemma for twice differentiable functions involving Riemann-Liouville(R-L) fractional integral operator. On the basis of this newly developed lemma, we make some new results regarding of this identity. These new results yield us some generalizations of the prior results. This study builds upon on a novel new auxiliary result which enables us to develop new variants of Ostrowski type inequalities for twice differentiable preinvex mappings. As an application, several estimates concerning Bessel functions of real numbers are also illustrated.</p></abstract>

Generalized weighted fractional Ostrowski type inequality with applications

Generalized weighted fractional Ostrowski type inequality with applications

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.

Some perturbed inequalities of Ostrowski type for twice differentiable functions

We establish new perturbed Ostrowski type inequalities for functions whose second derivatives are of bounded variation. In addition, we obtain some integral inequalities for absolutely continuous mappings. Finally, some inequalities related to Lipschitzian derivatives are given.

Fuzzy Ostrowski type inequalities via h-convex

We would like to state well-known Ostrowski inequality via h-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 h-convex by Holder’s and power mean inequalities. This class of h-convex function, which is the generalization of many important classes including class of Godunova-Levin s-convex, s-convex in the 2nd 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.

Extensions of Ostrowski Type Inequalities via h -Integrals and s-Convexity

In this paper, Hölder, Minkowski, and power mean inequalities are used to establish Ostrowski type inequalities for s -convex functions via h -calculus. The new inequalities are generalized versions of Ostrowski type inequalities available in literature.

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.

Some generalized fractional trapezoid and Ostrowski type inequalities for functions with bounded partial derivatives

In this paper, we first prove three identities for twice partially differentiable functions. Then, by using these equalities, we obtain several trapezoid and Ostrowski type inequalities via generalized fractional integrals for functions with bounded partial derivatives. Moreover, we present some results for Riemann‐Liouville fractional integrals by special choice of main results.

New Ostrowski-Type Fractional Integral Inequalities via Generalized Exponential-Type Convex Functions and Applications

Recently, fractional calculus has been the center of attraction for researchers in mathematical sciences because of its basic definitions, properties and applications in tackling real-life problems. The main purpose of this article is to present some fractional integral inequalities of Ostrowski type for a new class of convex mapping. Specifically, n–polynomial exponentially s–convex via fractional operator are established. Additionally, we present a new Hermite–Hadamard fractional integral inequality. Some special cases of the results are discussed as well. Due to the nature of convexity theory, there exists a strong relationship between convexity and symmetry. When working on either of the concepts, it can be applied to the other one as well. Integral inequalities concerned with convexity have a lot of applications in various fields of mathematics in which symmetry has a great part to play. Finally, in applications, some new limits for special means of positive real numbers and midpoint formula are given. These new outcomes yield a few generalizations of the earlier outcomes already published in the literature.

New Modifications of Integral Inequalities via ℘-Convexity Pertaining to Fractional Calculus and Their Applications

Integral inequalities for ℘-convex functions are established by using a generalised fractional integral operator based on Raina’s function. Hermite–Hadamard type inequality is presented for ℘-convex functions via generalised fractional integral operator. A novel parameterized auxiliary identity involving generalised fractional integral is proposed for differentiable mappings. By using auxiliary identity, we derive several Ostrowski type inequalities for functions whose absolute values are ℘-convex mappings. It is presented that the obtained outcomes exhibit classical convex and harmonically convex functions which have been verified using Riemann–Liouville fractional integral. Several generalisations and special cases are carried out to verify the robustness and efficiency of the suggested scheme in matrices and Fox–Wright generalised hypergeometric functions.

On some new Ostrowski type inequalities for co-ordinated s-Godunova-Levin convex functions in thesecond sense

On some new Ostrowski type inequalities for co-ordinated s-Godunova-Levin convex functions in thesecond sense

A note on some Ostrowski type inequalities via Generalized Exponentially Convexity

In this paper, we define and investigate generalized exponential type convex functions namely exponentially $s$--convex function. In the support of this newly introduced idea, we attain the algebraic properties of this function, and furthermore, in the frame of simple calculus, we explore and attain the novel kind of Ostrowski type inequalities.

Some Ostrowski Type Integral Inequalities using Hypergeometric Functions

The main objective of this paper is basically to acquire some new extensions of Ostrowski type inequalities for the function whose first derivatives' absolute value are $s$--type $p$--convex. We initially presented a new auxiliary definition namely $s$--type $p$--convex function. Some beautiful algebraic properties and examples related to the newly introduced definition are discussed. We additionally investigated some beautiful cases that can be derived from the novel refinements of the paper. These new results yield us some generalizations of the prior results. We trust that the techniques introduced in this paper will further motivate intrigued researchers.