On approximation in the Bers spaces

On Approximation in the Bers Spaces

Let D be a Jordan domain in the complex plane with rectifiable boundary C. Let Aq(D) denote the Bers space with norm || ||,. We prove that if/6 A„(D), 2<q<cc, then there exist functions ■s„W = 2£=i l/(z — zn!c), znltEC for k = \,■ ■ ,n, such that \Un— f\\«—"-0This result does not hold for 1 <q^2 even when D is a disc.

On the Bers Fiber Spaces

It is well known that a Bers fiber space F (Γ) for a torsion free finitely generated Fuchsian group Γ of the first kind can be identified with a Teichmüller space. If Γ has torsion, a theorem of Earle–Kra [9] asserts that in almost all cases, F (Γ) is not isomorphic to any Teichmüller space. However, there are 39 cases which remain unsettled. Our results remove 27 from the 39 previously unknown...

Some Results on p-Best Approximation in Vector Spaces

BEST SIMULTANEOUS APPROXIMATION IN FUZZY NORMED SPACES

The main purpose of this paper is to consider the t-best simultaneousapproximation in fuzzy normed spaces. We develop the theory of t-bestsimultaneous approximation in quotient spaces. Then, we discuss the relationshipin t-proximinality and t-Chebyshevity of a given space and its quotientspace.

t-BEST APPROXIMATION IN FUZZY NORMED SPACES

The main purpose of this paper is to find t-best approximations in fuzzy normed spaces. We introduce the notions of t-proximinal sets and F-approximations and prove some interesting theorems. In particular, we investigate the set of all t-best approximations to an element from a set.