Best Simultaneous Approximation in Orlicz 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.

Research Article Best Simultaneous Approximation in Orlicz Spaces

Recommended by Ricardo Estrada Let X be a Banach space and let L Φ (I,X) denote the space of Orlicz X-valued integrable functions on the unit interval I equipped with the Luxemburg norm. In this paper, we present a distance formula dist Φ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in a...

One-complemented subspaces of Musielak-Orlicz sequence spaces

The aim of this paper is to characterize one-complemented subspaces of finite codimension in the Musielak–Orlicz sequence space l . We generalize the well-known fact (Ann. Mat. Pura Appl. 152 (1988) 53; Period. Math. Hungar. 22 (1991) 161; Classical Banach Spaces I, Springer, Berlin, 1977) that a subspace of finite codimension in lp, 1 p<∞, is one-complemented if and only if it can be expressed...

Some Results on p-Best Approximation in Vector Spaces

Fuzzy Best Simultaneous Approximation of a Finite Numbers of Functions

Fuzzy best simultaneous approximation of a finite number of functions is considered. For this purpose, a fuzzy norm on $Cleft (X, Y right )$ and its fuzzy dual space and also the  set of subgradients of a fuzzy norm are introduced. Necessary case of a proved theorem about characterization of simultaneous approximation will be extended to the fuzzy case.