Nenad Ujević

A method for solving nonlinear equations

A method for finding a solution of the equation f(x) = 0 is presented. The method is based on some specially derived quadrature rules. It is shown that the method can give better results than the Newton method.

Improvement and further generalization of inequalities of Ostrowski-Grüss type

Abstract 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.

New bounds for the first inequality of Ostrowski-Grüss type and applications

Abstract Some new bounds for the first inequality of Ostrowski-Gruss type are derived. These new bounds can be much better than some recently obtained bounds. Applications in numerical integration are also given.

A generalization of Ostrowski's inequality and applications in numerical integration

A new generalization of Ostrowskis integral inequality is established. A consequence of the generalization is that we can derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae. These estimates are improvements of some recently obtained estimates. Applications in numerical integration are also given.

Error inequalities for a generalized trapezoid rule

A generalized trapezoid rule is derived. Various error bounds for this rule are established.

New error bounds for the Simpson's quadrature rule and applications

New error bounds for the well-known Simpsons quadrature rule are derived. If we use these bounds then we can apply the Simpsons rule to functions whose first, second or third derivatives are unbounded below or above. Furthermore, these error bounds can be (much) better than some recently obtained bounds. Applications in numerical integration are also given.

A new iterative method for solving linear systems

Abstract A new iterative method for solving linear systems is derived. It can be considered as a modification of the Gauss–Seidel method. The modified method can be two times faster than the original one.

Generalizations of weighted version of Ostrowski's inequality and some related results.

We establish some new weighted integral identities and use them to prove a number of inequalities of Ostrowski type. Among other results, we generalize one result related to the weighted version of the Ostrowskis inequality of Pecaric and Savic (Zbornik radova VAKoV (Beograd), 9(1983), 171-202) as well as the recent result of Roumeliotis et al. (RGMIA, 1(1)(1998)). We also show that the recent Anastassious generalization (Proc. Amer. Math. Soc., 123(1995), 3775-3781) of the Ostrowskis inequality is a special case of some results from this paper.

Two sharp inequalities of Simpson type and applications

Abstract Two sharp inequalities of Simpson type are established. Applications in numerical integration are also given.

On generalizations of Ostrowski inequality and some related results

Some generalizations of the Ostrowski inequality, the Milovanović-Pečarić-Fink inequality, the Dragomir-Agarwal inequality and the Hadamard inequality are given.