On some geometric properties of suns

Nonlinear weighted best simultaneous approximation in Banach spaces

“…Then it is clear from the definition of a sun (cf. [3]) that G ⊆ X is an S-sun in X if and only if G is a sun in F . Thus if G is convex, then G is a sun in F .…”

“…The notion of suns in Banach spaces, which was introduced by Efimov and Stechkin in [9], has played important roles in nonlinear approximation theory in Banach spaces, see for example [3,4,9,32]. The following definition is an extension of the notion given in [3] to the case of simultaneous approximations, see [20].…”

“…The following definition is an extension of the notion given in [3] to the case of simultaneous approximations, see [20]. Definition 3.1.…”

Support cones and convexity of sets in ℝⁿ

“…In the mid 70's, Brosowski and Deutsch defined various types of radial continuity and showed how these are related to convexity [4], [5], [6]. The separate properties they defined were interesting in their own right and characterized certain phenomena.…”

Approximation properties of vector valued functions

“…(See Singer [15] and Brosowski and Deutsch). [2]. The present result was initiated by a proof of this special case by Strobele which was based upon the use of the Characterization Theorem (Theorem 4), and which was simplified by suggestions from Overdeck [16J, [10].…”