a polynomial and H. Sugiura Engineering, Faculty of Engineering, Nagoya University, Nagoya, 464-01, Japan Sakurai, T., T. Torii and H. Sugiura, A high-order iterative formula for simultaneous determination of zeros of a polynomial, Journal of Computational and Applied Mathematics 38 (1991) 387-397. We propose a hybrid method to determine all the zeros of a polynomial, simultaneously, by combini...

Let Pd denote the family of all polynomials of degree at most d in one variable x, with real coefficients. A sequence of positive numbers x1 ≤ x2 ≤ . . . is called Pd-controlling if there exist y1, y2, . . . ∈ R such that for every polynomial p ∈ Pd there exists an index i with |p(xi)−yi| ≤ 1. We settle an problem of Makai and Pach (1983) by showing that x1 ≤ x2 ≤ . . . is Pd-controlling if and...

We present existence of common fixed point results as best simultaneous approximation for uniformlyR-subweakly mappings on non-starshaped domains in convex spaces. This work provides extension as well as substantial improvement of some results in the existing literature. 2010 Mathematics Subject Classification: 41A50, 47H10, 54H25.

we study the theory of best approximation in tensor product and the direct sum of some lattice normed spacesx_{i}. we introduce quasi tensor product space anddiscuss about the relation between tensor product space and thisnew space which we denote it by x boxtimesy. we investigate best approximation in direct sum of lattice normed spaces by elements which are not necessarily downwardor upward a...

and Applied Analysis 3 So,

Let m,n be positive integers, and denote byMm,n the space of m×n matrices with real entries. Dirichlet’s Theorem (hereafter abbreviated by ‘DT’) on simultaneous diophantine approximation states that for any A ∈ Mm,n (viewed as a system of m linear forms in n variables) and for any T > 1 there exist q = (q1, . . . , qn) ∈ Z r {0} and p = (p1, . . . , pm) ∈ Z satisfying the following system of in...

Concept of locally ε-maximal is proposed and employed to explored the optimization problem of a set of convex functions on a Banach space in this paper. Generalized saddle point (GSP) is also used to study the optimization problem , which is equivalent to the optimal solution under the condition of locally ε-maximal. An application of the optimization theory to best simultaneous approximation i...

This brief survey deals with multi-dimensional Diophantine approximations in sense of linear form and with simultaneous Diophantine approximations. We discuss the phenomenon of degenerate dimension of linear sub-spaces generated by the best Diophantine approximations. Originally most of these results have been established by the author in [14, 15, 16, 17, 18]. Here we collect all of them togeth...