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A generalisation of the Ostrowski integral inequality for mappings of bounded variation and applications for general quadrature formulae are given.

Content uploaded by S. S. Dragomir

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All content in this area was uploaded by S. S. Dragomir on Apr 09, 2015

Content may be subject to copyright.

A preview of the PDF is not available

... The formula (1.4) was further studied in [2,3,4,5,6,8,9,10,16,20]. ...

... 10) holds and constant 1 in RHS is best possible, where .15. Clearly, when r = 1 in (1.10) we get (1.9). ...

The paper presents a novel approach to generalize the two-point weighted Ostrowski’s formula for Riemann-Stieltjes integrals by utilizing a unique class of functions of bounded rvariation. The proposed approach yields several results that exhibit sharp and better bounds compared to existing established results by using parameters and weights. Additionally, the paper also captures many of the known results as special cases.

... These features are more stylish than convex fuzzy features and while differentiable are fuzzy invex [4] . Studied on the deducement of Ostrowski Inequality considering Lipschitzan calculation and function tendency numerical search as well as considering Euler's beta inclined [5] . Established the advanced Ostrowski inequality and originates its conclusion to respect of the high and dip limits with derivative Also indicate a bit effort on Ostrowski inequality thoroughly continues function [6] . ...

The purpose of proceeding work is to form new generalized and extended form of Ostrowski type inequality by the help of fraction order integral of Katugampola type which is the extended form of Reimann-Liouville and Hadamard integral of fractional order. To get the results, a new identity is introduced by the researchers which help in deriving the few inequalities for the class of whose powers are absolute derivatives values are p-convex. It can be seen that the extended form is generalization of some well-known results.

... In 1938, the integral inequalities are established by Ukrainian Mathematician A. M. Ostrowski [1] named as Ostrowski's inequality. Dragomir gave the first generalization of integral inequalities for the function of bounded variation [12][13][14][15][16][17]. Several authors have worked on the Ostrowski's type inequalities for the function of bounded variation (see for example [9][10][11][18][19][20]). ...

In this paper, some new integral inequalities are developed by using a 7-step linear kernel for the function of bounded variation. Applications of quadrature rule and probability density function are also provided. We also constructed some generalized trapezoid and midpoint inequalities for the linear functions of bounded variations.

... In 1938, the integral inequalities are established by Ukrainian Mathematician A. M. Ostrowski [1] named as Ostrowski's inequality. Dragomir gave the first generalization of integral inequalities for the function of bounded variation [12][13][14][15][16][17]. Several authors have worked on the Ostrowski's type inequalities for the function of bounded variation (see for example [9][10][11][18][19][20]). ...

In this paper, some new integral inequalities are developed by using a 7-step linear kernel for the function of bounded variation. Applications of quadrature rule and probability density function are also provided. We also constructed some generalized trapezoid and midpoint inequalities for the linear functions of bounded variations.

In this work, we introduced the Ostrowski inequality based on M-fractional integrals. we initially established an identity concerning this inequality to prove the Ostrowski inequality based on M-fractional integrals. We derive some results for the Ostrowski inequality utilizing this identity, different convex of classes of functions, and well-known inequalities.

The nonlinear conformable model that arises in plasma physics is the 3D conformable Zakharov-Kuznetsov equation (CZKE) with power law nonlinearity (PLNL). The current study applies a modification of the (𝐺𝐺′/𝐺𝐺)-expansion (𝑀𝑀𝑀𝑀′/𝐺𝐺𝐺𝐺) approach to this model and obtains certain closed-form precise wave
olutions. By going backwards into the 3D CZKE with PLNL, the obtained results are confirmed, and they are noted as being particularly advantageous over a
number of current methods. For the other nonlinear conformable models in physics, mathematics, and engineering, the aforementioned approach could also be used to obtain closed-form wave solutions.

In this chapter we establish some Ostrowski and generalized trapezoid type inequalities for the Riemann-Liouville fractional integrals of functions of bounded variation and of Lipschitzian functions. Applications for mid-point and trapezoid inequalities are provided as well. They generalize the know results holding for the classical Riemann integral.

In this paper, we establish some Ostrowski type integral inequalities for functions of two variables involving generalized fractional integrals. The results presented here provide extensions of those given in earlier works.

In this paper, three-point quadrature rules for the Riemann-Stieltjes integral are introduced. Some inequalities of Ostrowski's type are also obtained.

In this paper we prove a new Ostrowski's inequality in $L_1$-norm and apply it to the estimation of error bounds for some special means and for some numerical quadrature rules.

In this paper we derive a new inequality of Ostrowski-Grüss' type and apply it to the estimation of error bounds for some special means and for some numerical quadrature rules.

In this paper, we present a new proof to the classical Ostrowski's inequality and apply it to the estimation of error bounds for some special means and for some numerical quadrature rules.

This Chapter is devoted to various unconnected results which do not easily relate to the types we have presented in the previous chapters. A derivative or integral of a function of one or two variables appear in each inequality of this Chapter.

I. Landau-Kolmogorov and related inequalities.- II. An inequality ascribed to Wirtinger and related results.- III. Opial's inequality.- IV. Hardy's, Carleman's and related inequalities.- V. Hilbert's and related inequalities.- VI. Inequalities of Lyapunov and of De la Vallee Poussin.- VII. Zmorovi?'s and related inequalities.- VIII. Carlson's and related inequalities.- IX. Inequalities involving kernels.- X. Convolution, rearrangement and related inequalities.- XI. Inequalities of Caplygin type.- XII. Inequalities of Gronwall type of a single variable.- XIII. Gronwall inequalities in higher dimension.- XIV. Gronwall inequalities on other spaces: discrete, functional and abstract.- XV. Integral inequalities involving functions with bounded derivatives.- XVI. Inequalities of Bernstein-Mordell type.- XVII. Methods of proofs for integral inequalities.- XVIII. Particular inequalities.- Name Index.

A generalization of Ostrowski integral inequality for mappings whose derivatives belong to L_1 [a,b], and applications for general quadrature formulae are given.