In this paper, we obtain several new continuous selection theorems for multi-valued mappings on completely regular spaces and fixed point theorems for multi-valued maps on nonmetrizable spaces. They, in particular, provide a partial solution of a conjecture of X. Wu.

In this paper, we introduce a broad class of nonlinear mappings in a Hilbert space which covers nonexpansive mappings, nonspreading mappings, hybrid mappings and contractive mappings. Then we prove fixed point theorems for the class of such mappings. Using these results, we prove well-known and new fixed point theorems in a Hilbert space.

In this note, we will discuss what kind of operators between C*-algebras preserves Jordan triple products

We prove that log n is an almost everywhere convergence Weyl multiplier for the orthonormal systems of non-overlapping Haar polynomials. Moreover, it is done for the general systems of martingale difference polynomials.

Let <i>M</i> be a compact connected (topological) manifold of finite- or infinite-dimension <i>n</i>. Let 0 <i>r</i> 1 be arbitrary but fixed. We construct in this paper a space-filling curve <i>f</i> from [0,1] onto <i>M</i>, under which <i>M</i> is the image of a compact set <i>A</i> of Hausdorff dimension <i>r</i>. Moreover, the restriction of f to <i>A</i> is one-to-one over the image of a dense subset provided that 0 <i>r</i> log|2^<i>n</i>/log(2^<i>n</i> + 2). The proof is based on the special case where <i>M</i> is the Hilbert cube [0,1].