Some Further Generalizations of Ky Fan′s Best Approximation Theorem

Applications and Generalizations of the Approximation Theorem

In its basic form, the approximation theorem referred to provides simple n n combinatorial models for spaces ~ E X, where X is a connected based space. The first such result was given by James [26], who showed that ~EX is equivalent to the James construction MX. The unpublished preprint form of Dyer and gashof's paper [25] gave an approximation to QX = lira ~nEnx, and Milgram [41] gave a cellul...

Some further results on the stability of Ky Fan’s points

In this paper, some further results on the stability of Ky Fan's points are proposed by introducing a type of stronger perturbation of section mappings defined by a semi-metric called the maximum Hausdorff semi-metric, and the existence of the essential components of the set of Ky Fan's points to this perturbation is proved. As an application, the existence of the essential component of the Nas...

Some Generalizations of Fedorchuk Duality Theorem – I

Generalizing Duality Theorem of V. V. Fedorchuk [11], we prove Stone-type duality theorems for the following four categories: all of them have as objects the locally compact Hausdorff spaces, and their morphisms are, respectively, the continuous skeletal maps, the quasi-open perfect maps, the open maps, the open perfect maps. In particular, a Stone-type duality theorem for the category of all c...

Some generalizations of the MacMahon Master Theorem

We consider a number of generalizations of the β-extended MacMahon Master Theorem for a matrix. The generalizations are based on replacing permutations on multisets formed from matrix indices by partial permutations or derangements over matrix or submatrix indices.

Some Generalizations of Jungck's Fixed Point Theorem