Lipschitz continuity of the best approximation operator in vector-valued Chebyshev approximation

Some Results on p-Best Approximation in Vector Spaces

Best Approximation in TVS

In this paper  we give newresults on the best approximation  in the Hausdorff topological vectorspace and  consider relationship  with orthogonality. Also we determined under  what conditions the map $P_{K,f}$ is upper semicontinous.

Continuity Properties of Best Analytic Approximation

Let A be the operator which assigns to each m×n matrix-valued function on the unit circle with entries in H∞+C its unique superoptimal approximant in the space of bounded analytic m × n matrix-valued functions in the open unit disc. We study the continuity of A with respect to various norms. Our main result is that, for a class of norms satifying certain natural axioms, A is continuous at any f...

Best Lipschitz constant of the trapezoidal approximation operator preserving the expected interval

In this paper, we prove new distance properties between a fuzzy number and its trapezoidal approximation preserving the expected interval. Then, we find the best Lipschitz constant of the trapezoidal approximation operator preserving the expected interval. Finally, we use this result in finding within a reasonable error the trapezoidal approximation of a fuzzy number preserving the expected int...

Second dual space of little $alpha$-Lipschitz vector-valued operator algebras

Let $(X,d)$ be an infinite compact metric space, let $(B,parallel . parallel)$ be a unital Banach space, and take $alpha in (0,1).$ In this work, at first we define the big and little $alpha$-Lipschitz vector-valued (B-valued) operator algebras, and consider the little $alpha$-lipschitz $B$-valued operator algebra, $lip_{alpha}(X,B)$. Then we characterize its second dual space.