Nazir Ahmad Mir

Some quadrature based three-step iterative methods for non-linear equations

In this paper, we present three-step quadrature based iterative methods for solving non-linear equations. The convergence analysis of the methods is discussed. It is established that the new methods have convergence order six, seven and eight respectively. Numerical tests show that the new methods are comparable with the well known existing methods and in many cases give better results. Our results can be considered as an improvement and refinement of the previously known results in the literature.

A Generalized Ostrowski Type Inequality for a Random Variable Whose Probability Density Function Belongs to L ∞ [a,b]

Abstract We establish here an inequality of Ostrowski type for a random variable whose probability density function belongs to Lp[a, b], in terms of the cumulative distribution function and expectation. The inequality is then applied to generalized beta random variable.

A third-order convergent iterative method for solving non-linear equations

In this paper, we present and analyse a new predictor-corrector iterative method for solving non-linear single variable equations. The convergence analysis establishes that the new method is cubically convergent. Numerical tests show that the method is comparable with the well-known existing methods and in many cases gives better results.

Some Generalized Error Inequalities and Applications

We present a family of four-point quadrature rule, a generalization of Gauss-two point, Simpsons , and Lobatto four-point quadrature rule for twice-differentiable mapping. Moreover, it is shown that the corresponding optimal quadrature formula presents better estimate in the context of four-point quadrature formulae of closed type. A unified treatment of error inequalities for different classes of function is also given.

SOME NEW ČEBYŠEV TYPE INEQUALITIES

Some new Cebysev type inequalities have been developed by working on functions whose first derivatives are absolutely continuous and the second derivatives belong to the usual Lebesgue space L∞ [a, b] . A unified treatment of the special cases is also given.

A Note on the Generalization of Some New ˘Ceby˘sev Type Inequalities

In this paper, we present a generalized Ceby?ev type inequality for absolutely continuous functions whose derivatives belong to L(subscript p) [a, b], p＞1. Applications for probabilty density functions are also given.

Fourth Order Methods for Finding Multiple as well as Distinct Zeros of Non-linear Equations

In this paper, we point out and analyse six two-step iterative methods for finding multiple as well as distinct zeros of non-linear equations. We prove that the methods for multiple zeros as well as for distinct zeros have fourth order convergence. The methods calculate the multiple as well as distinct zeros with high accuracy. The numerical tests show their better performance in case of algebraic as well as non-algebraic equations.

SOME INEQUALITIES OF ACZEL TYPE FOR GRAMIANS IN n-INNER PRODUCT SPACES

Some inequalities of Aczel type for Gramians in n—inner product spaces which generalize pecaric result for n—inner product spaces are given. Applications connected to Schwartzs inequality for n—inner product spaces are also noted.