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.

the aim of this paper is to give the set of all t -best approximations on fuzzy n-normed spaces and prove some theorems in the sense of vaezpour and karimi [13].

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...

The existence of common fixed points is established for three mappings where T is either generalized (f, g)-nonexpansive or asymptotically (f, g)-nonexpansive on a set of fixed points which is not necessarily starshaped. As applications, the invariant best simultaneous approximation results are proved. AMS subject classifications: 47H10, 54H25

and Applied Analysis 3 So,

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...