The critical numbers for unsymmetrical approximation

The Critical Numbers for Unsymmetrical Approximation

Unsymmetrical Approximation of Irrational Numbers

1 A 1 < £ < , 5B B SB so that we have the classical theorem of Hurwitz. For other values of r, approximations from both sides are permitted, but the errors allowed on the two sides are different; hence the term unsymmetrical approximation. The result here was new, and is so related to Hurwitz's inequality that one side is strengthened and the other weakened. Notice that the result for r > l is ...

Width invariant approximation of fuzzy numbers

In this paper, we consider the width invariant trapezoidal and triangularapproximations of fuzzy numbers. The presented methods avoid the effortful computation of Karush-Kuhn-Tucker Theorem. Some properties of the new approximation methods are presented and the applicability of the methods is illustrated by examples. In addition, we show that the proposed approximations of fuzzy numbers preserv...

Close interval approximation of piecewise quadratic fuzzy numbers for fuzzy fractional program

  The fuzzy approach has undergone a profound structural transformation in the past few decades. Numerous studies have been undertaken to explain fuzzy approach for linear and nonlinear programs. While, the findings in earlier studies have been conflicting, recent studies of competitive situations indicate that fractional programming problem has a positive impact on comparative scenario. We pro...

On the Approximation to Algebraic Numbers by Algebraic Numbers

Let n be a positive integer. Let ξ be an algebraic real number of degree greater than n. It follows from a deep result of W. M. Schmidt that, for every positive real number ε, there are infinitely many algebraic numbers α of degree at most n such that |ξ−α| < H(α)−n−1+ε, where H(α) denotes the näıve height of α. We sharpen this result by replacing ε by a function H 7→ ε(H) that tends to zero wh...