Radial continuity of set-valued metric projections

Common Fixed Point Theorem for Occasionally Weakly Baised Mappings and Its Application to Best Approximation

“…Many authors have studied the applications of fixed point theorems to best approximation theory including [2], [3], [5], [6]- [8], [10], [16], [18], [19], [22], [23], [25]- [34].…”

An application of fixed point theorems in best approximation theory

“…By relaxing the linearity of the operator T and the convexity of D in the original statement of Brosowski [1], Singh [10] In the subsequent paper [11], Singh observed that only the nonexpansiveness of T on D' DU{} is necessary. Further, Hicks and Humphries [4] have shown that the assumption T" C C can be weakened to the condition T" OC C if y C, i.e., y E D is not necessarily in the interior of C, where OC denotes the boundary of C. Theorem 2.…”

“…For a 1, our definition reduces to the set D of best C-approximants to . A subset C of X is said to be starshaped with, respect to a point q E C if, for all x in C and all A 5 [1,0] {0} is starshaped with respect to (0, 0) e C as the star-centre of C, but it is not convex.…”

Best approximations, fixed points and parametric projections

“…In the classical theory of best approximation, the approximating set is fixed, here we allow both the approximating set and the point that is being approximated to vary (as recently in [1] and in [11]). In particular, we prove the continuity of the parametric projection ℘ .…”