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Grüss inequality is subject of interest for many authors due to its effectiveness in predicting bounds in several quadrature problems. In the present article, we give weighted treatment of the discrete Čebyšev and Grüss type inequalities pertaining two n-tuples of real numbers in which the bounding constants are mobilised with bounding sequences of real numbers. As an application estimations of discrete Ostrowski type inequalities are provided. Finally, by practicing obtained results along with Jensen's difference, a wide range of estimations are formalised by considering Jensen-Grüss differences. [ABSTRACT FROM AUTHOR]

New upper bounds for the weighted Chebyshev functional under various conditions, including those of Steffensen type, are given. The obtained results are used to establish some new bounds for the Jensen functional.

This paper aims to extend the application of the Ostrowski inequality, a crucial tool for figuring out the error bounds of various numerical quadrature rules, including Simpson's, trapezoidal, and midpoint rules. Specifically, we develop a more comprehensive class of Ostrowski-type inequalities by utilizing the weighted version of Riemann–Liouville (RL) fractional integrals on an increasing function. We apply our findings to estimate the error bounds of Hadamard-type inequalities. Our results are more comprehensive, since we obtain the results of the existing literatures as particular cases for certain parameter values. This research motivates researchers to apply this concept to other fractional operators. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new Hermite-Hadamard type inequality by using post-quantum calculus for s-preinvex function and establish a new (p,q)-integral identity to derive some new Ostrowski type inequality for (p,q)-differentiable function. We give some application to special means for our newly proved inequalities. [ABSTRACT FROM AUTHOR]

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.

In this paper, using the quantum derivatives and quantum integrals, we prove some new quantum Ostrowski's type inequalities for pre-invex functions. Furthermore, in the special cases of newly developed inequalities, we obtain different new and existing Ostrowski's type inequalities. [ABSTRACT FROM AUTHOR]

Let f be an operator monotonic function on I and A, B∈I (H), the class of all selfadjoint operators with spectra in I. Assume that p : [0.1], →ℝ is non-decreasing on [0, 1]. In this paper we obtained, among others, that for A ≤ B and f an operator monotonic function on I,

In the current paper, a generalized Montgomery identity is obtained with the help of Taylor's formula on time scales. The obtained identity is used to establish Ostrowski inequality, mid-point inequality, and trapezoid inequality. Moreover, the weighted versions of generalized Montgomery identity and respective Ostrowski inequality are also discussed. Special cases are obtained for different time scales to obtain new and existing results. [ABSTRACT FROM AUTHOR]

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 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. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new concept k- β -convex functions and establish some new Ostrowski's inequalities for functions whose derivative modulus is k- β -convex via Riemann–Liouville k-fractional integrals. [ABSTRACT FROM AUTHOR]

We establish two Ostrowski type inequalities for double integrals of second order partial derivable functions which are bounded. Then, we deduce some inequalities of Hermite-Hadamard type for double integrals of functions whose partial derivatives in absolute value are convex on the co-ordinates on rectangle from the plane. Finally, some applications in Numerical Analysis in connection with cubature formula are given.

In this article, we develop a novel framework to study a new class of convex functions known as n-polynomial 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 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. [ABSTRACT FROM AUTHOR]

In this study, we prove an identity for twice partially differentiable mappings involving the double generalized fractional integral and some parameters. By using this established identity, we offer some generalized inequalities for differentiable co-ordinated convex functions with a rectangle in the plane R 2 . Furthermore, by special choice of parameters in our main results, we obtain several well-known inequalities such as the Ostrowski inequality, trapezoidal inequality, and the Simpson inequality for Riemann and Riemann–Liouville fractional integrals. [ABSTRACT FROM AUTHOR]

Inequality theory provides a significant mechanism for managing symmetrical aspects in real-life circumstances. The renowned distinguishing feature of integral inequalities and fractional calculus has a solid possibility to regulate continuous issues with high proficiency. This manuscript contributes to a captivating association of fractional calculus, special functions and convex functions. The authors develop a novel approach for investigating a new class of convex functions which is known as an n-polynomial P -convex function. Meanwhile, considering two identities via generalized fractional integrals, provide several generalizations of the Hermite–Hadamard and Ostrowski type inequalities by employing the better approaches of Hölder and power-mean inequalities. By this new strategy, using the concept of n-polynomial P -convexity we can evaluate several other classes of n-polynomial harmonically convex, n-polynomial convex, classical harmonically convex and classical convex functions as particular cases. In order to investigate the efficiency and supremacy of the suggested scheme regarding the fractional calculus, special functions and n-polynomial P -convexity, we present two applications for the modified Bessel function and q -digamma function. Finally, these outcomes can evaluate the possible symmetric roles of the criterion that express the real phenomena of the problem. [ABSTRACT FROM AUTHOR]

In this work we obtain some new generalized fractional Montgomery identities for Katugampola fractional integral operator. Then, using these identities, we establish some new Ostrowski type inequalities. [ABSTRACT FROM AUTHOR]

The celebrated Hermite–Hadamard and Ostrowski type inequalities have been studied extensively since they have been established. We find novel versions of the Hermite–Hadamard and Ostrowski type inequalities for the n-polynomial s-type convex functions in the frame of fractional calculus. Taking into account the new concept, we derive some generalizations that capture novel results under investigation. We present two different general techniques, for the functions whose first and second derivatives in absolute value at certain powers are n-polynomial s-type convex functions by employing K -fractional integral operators have yielded intriguing results. Applications and motivations of presented results are briefly discussed that generate novel variants related to quadrature rules that will be helpful for in-depth investigation in fractal theory, optimization and machine learning. [ABSTRACT FROM AUTHOR]

Based on the theory of local fractional calculus and generalized harmonically convex function on fractal sets, the author establishes a general identity involving local fractional integrals. Using this identity, some inequalities on generalization of Hermite-Hadamard, Ostrowski and Simpson type inequalities for functions whose absolute values of derivatives are generalized harmonically convex function involving local fractional integrals are obtained. Finally, some applications of these inequalities for α-type special means are given. [ABSTRACT FROM AUTHOR]

We obtained useful identities via Fink's identity, by which the inequality of Popoviciu for convex functions is generalized for higher order convex functions. We investigate the bounds for the identities related to the generalization of the Popoviciu inequality using inequalities for the Čebyšev functional. Some results relating to the Grüss- and Ostrowski-type inequalities are constructed. Further, we also construct new families of exponentially convex functions and Cauchy-type means by looking at linear functional associated with the obtained inequalities. [ABSTRACT FROM AUTHOR]

In this paper, we define some integral transforms and obtain suitable bounds for them in order to introduce a main class of integral inequalities including Ostrowski and Ostrowski-Grüss inequalities and various kinds of new integral inequalities. In this sense, we also introduce a three point quadrature formula and obtain its error bounds. [ABSTRACT FROM PUBLISHER]

We establish an Ostrowski type inequality for mappings whose second derivatives are bounded, then some results of this inequality that are related to previous works are given. Finally, some applications of these inequalities in numerical integration and for special means are provided. [ABSTRACT FROM PUBLISHER]

In this paper, a new general identity for fractional integrals have been defined. By using of this identity, new estimates on generalization of Hadamard, Ostrowski and Simpson like type inequalities for harmonically quasi-convex functions via the Riemann–Liouville fractional integral have been obtained. [ABSTRACT FROM AUTHOR]

We provide new inequalities of Jensen-Ostrowski type, by considering bounds for the magnitude of $\int_{\Omega} f\circ g \, d\mu-f ( \zeta ) - ( \int_{\Omega }g\, d\mu-\zeta ) f^{\prime} ( \zeta ) -\frac {1}{2}\lambda \int_{\Omega} ( g-\zeta ) ^{2}\, d\mu$, $\zeta\in [a,b]$, with various assumptions on the absolutely continuous function $f:[a,b]\rightarrow\mathbb{C}$ and a μ-measurable function g, and a complex number λ. Inequalities of Ostrowski and Jensen type are obtained as special cases, by setting $\lambda=0$ and $\zeta =\int_{\Omega}g\, d\mu$, respectively. In particular, we obtain some bounds for the discrepancy in Jensen's integral inequality. Applications of these inequalities for f-divergence measures are also given. [ABSTRACT FROM AUTHOR]

In this paper, we provide inequalities of Jensen–Ostrowski type, by providing bounds for the magnitude of ∫ Ω ( f ∘ g ) d μ − f ( ζ ) − ∫ Ω ( g − ζ ) f ′ ∘ g d μ + 1 2 λ ∫ Ω ( g − ζ ) 2 d μ , for various assumptions on the absolutely continuous function f : [ a , b ] → C , ζ ∈ [ a, b ], λ ∈ C , and a μ -measurable function g on Ω . Special cases are considered to provide some inequalities of Jensen type, as well as Ostrowski type, in measure-theoretic (probabilistic) form. Applications for f -divergence measure in information theory are also considered. [ABSTRACT FROM AUTHOR]

In this paper, we establish several new inequalities for s-convex mappings that are connected with the Riemann-Liouville fractional integrals. Our results have some relationships with an Ostrowski type integral inequality in the literature. [ABSTRACT FROM AUTHOR]

We present a weighted Montgomery identity for the fractional integral of a function f with respect to another function g and use it to obtain weighted Ostrowski type inequalities for fractional integrals involving functions whose first derivatives belong to Lp spaces. These inequalities are generally sharp in case and best possible in case . Applications for the Hadamard fractional integrals are given. [ABSTRACT FROM AUTHOR]

We develop weighted generalization of the recently obtained Ostrowski type inequalities for continuous functions with eventually one point of non-differentiability. We apply these general result for some famous weight functions. [ABSTRACT FROM AUTHOR]

In this paper we first derive an Ostrowski type inequality on time scales for double integrals via ΔΔ-integral which unify corresponding continuous and discrete versions. We then replace the ΔΔ-integral by the ∇ ∇-, Δ ∇-, and ∇Δ-integrals and get completely analogous results. [ABSTRACT FROM AUTHOR]

New very general univariate Ostrowski-type inequalities are established, involving the and , , norms of the engaged nth order derivative, . In establishing them, several important new univariate identities of Montgomery type are developed and presented for the first time. [ABSTRACT FROM AUTHOR]

An Ostrowski type integral inequality for the Riemann-Stieltjes integral ∫abƒ (t) du (t), where ƒ is assumed to be of bounded variation on [a,b] andu is ofr-H- Hölder type on the same interval, is given. Applications to the approximation problem of the Riemann-Stieltjes integral in terms of Riemann-Stieltjes sums are also pointed out. [ABSTRACT FROM AUTHOR]

An Ostrowski type integral inequality for the Riemann-Stieltjes integral ∫ ƒ (t) du ( t), where ƒ is assumed to be of bounded variation on [a, b] and u is of r- H- Hölder type on the same interval, is given. Applications to the approximation problem of the Riemann-Stieltjes integral in terms of Riemann-Stieltjes sums are also pointed out. [ABSTRACT FROM AUTHOR]

In the article, we establish several Ostrowski type inequalities involving the conformable fractional integrals. As applications, we find new inequalities for the arithmetic and generalized logarithmic means. [ABSTRACT FROM AUTHOR]

Abstract: On utilizing a generalization of the weighted Montgomery identity obtained by Barnett and Dragomir [published in N.S. Barnett, S.S. Dragomir, On the weighted inequalities, J. Inequal. Pure Appl. Math. 8 (4) (2007) Art. 96], new weighted Ostrowski and Čebyšev type inequalities are established. [Copyright &y& Elsevier]