List of Figures List of Tables Preface List of Symbols 1 Generalizations of the Ostrowski Inequality and Applications SS Dragomir, TM Rassias 2 Integral Inequalities for eta-Times Differentiable Mappings A Sofo 3 Three Point Quadrature Rules P Cerone, SS Dragomir 4 Product Branched Peano Kernels and Numerical Integration P Cerone 5 Ostrowski Type Inequalities for Multiple Integrals NS Barnett, et al 6 Results for Double Integrals Based on an Ostrowski Type Inequality G Hanna 7 Product Inequalities and Weighted Quadrature J Roumeliotis 8 Some Inequalities for the Riemann-Stieltjes Integral SS Dragomir, TM Rassias Index

Ostrowski type inequalities and applications in numerical integration

Different from gradient-based neural dynamics, a special kind of recurrent neural dynamics has recently been proposed by Zhang et al for solving online time-varying problems Such a recurrent neural dynamics is designed based on an indefinite error-monitoring function instead of a usually norm- or square-based energy function In addition, Zhang neural dynamics (ZND) are depicted generally in implicit dynamics, whereas gradient-based neural dynamics (GND) are associated with explicit dynamics In this paper, we generalize the ZND design method to solving online nonlinear time-varying equations in the form of f (x, t) = 0 For comparative purposes, the GND model is also employed for such time-varying equations’ solving Computer-simulation results via power-sigmoid activation functions substantiate the theoretical analysis and efficacy of the ZND model for solving online nonlinear time-varying equations

Comparison on Zhang neural dynamics and gradient-based neural dynamics for online solution of nonlinear time-varying equation

The article investigates trapezoid type rules and obtains explicit bounds through the use of a Peano kernel approach and the modern theory of inequalities. Both Riemann-Stieltjes and Riemann integrals are evaluated with a variety of assumptions about the integrand enabling the characterisation of the bound in terms of a variety of norms. Perturbed quadrature rules are obtained through the use of Gruss, Chebychev and Lupas inequalities, producing a variety of tighter bounds. The implementation is demonstrated through the investigation of a variety of composite rules based on inequalities developed. The analysis allows the determination of the partition required that would assure that the accuracy the result would be within a prescribed error tolerance.

Trapezoidal Type Rules from an Inequalities Point of View

Midpoint-Type Rules from an Inequalities Point f View

In this note, we establish an inequality of Ostrowski-type involving functions of two independent variables newly by using certain integral inequalities.

http://www.iam.fmph.uniba.sk/amuc/_vol-79/_no_1/_sarikaya/sarikaya.pdf

On the ostrowski type integral inequality

An iterative method for solving nonlinear equations

We improve some inequalities of Ostrowski-Gruss type and further generalize them. We apply the obtained results to the estimation of error bounds for some numerical quadrature rules. Also, some bounds for the differences of some special means are discussed.

Improvement and further generalization of inequalities of Ostrowski-Grüss type

A method for solving nonlinear equations

We provide generalizations and improvements of a variety of recent results for the Ostrowski and Simpson inequalities. Mathematics subject classification (1991): 26D10.

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Generalizations of some inequalities of Ostrowski-Grüss Type

[1] M. ABRAMOWITZ AND I. A. STEGUN (Eds), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series 55, 4th printing, Washington, 1965. [2] S. S. DRAGOMIR, New estimation of the Remainder in Taylor’s Formula Using Gruss’ Type Inequalities and Applications, Math. Inequal. Appl. 2 (2) (1999), 183–193. [3] J. E. PECARIC, F. PROSCHAN AND Y. L. TONG, Convex Functions, Partial Orderings, and Statistical Applications, Academic Press, 1992.

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Nenad Ujević

Papers

An iterative method for solving nonlinear equations

Improvement and further generalization of inequalities of Ostrowski-Grüss type

A method for solving nonlinear equations

Generalizations of some inequalities of Ostrowski-Grüss Type

On new estimation of the remainder in generalized taylor's formula