Let and be a real uniformly smooth Banach space. Let be a nonempty closed convex subset of and be a strictly pseudocontractive mapping in the sense of FE Browder and WV Petryshyn [1]. Let be a bounded sequence in and be real sequences in satisfying some restrictions. Let be the bounded sequence in generated from any given by the Ishikawa iteration method with errors: , , . It is shown in this paper that if is compact or demicompact, then converges strongly to a fixed point of .

We study the following generalized quasivariational inequality problem: given a closed convex set <i>X</i> in a normed space <i>E</i> with the dual <i>E</i> ^*, a multifunction \Phi :Xightarrow 2^{E^{*}} and a multifunction :<i>X</i>2^<i>X</i>, find a point \Phi :Xightarrow 2^{E^{*}} such that \Phi :Xightarrow 2^{E^{*}} , \Phi :Xightarrow 2^{E^{*}} . We prove some existence theorems in which may be discontinuous, <i>X</i> may be unbounded, and is not assumed to be Hausdorff lower semicontinuous.

We analyze a family of singular Schrdinger operators describing a Neumann waveguide with a periodic array of singular traps of a delta\prime type. We show that in the limit when perpendicular size of the guide tends to zero and the delta\prime interactions are appropriately scaled, the first spectral gap is determined exclusively by geometric properties of the traps.

For an arbitrary nonempty, open set ^<i>n</i>, <i>n</i> of finite (Euclidean) volume, we consider the minimally defined higher-order Laplacian (-\Delta)^m|_{{C^\infty_0}(\Omega)}, <i>m</i> , and its Kreinvon Neumann extension <i>A</i>_{<i>K</i>,,<i>m</i>} in <i>L</i>²(). with <i>N</i>(, <i>A</i>_{<i>K</i>,,<i>m</i>)}, (-\Delta)^m|_{{C^\infty_0}(\Omega)}, denoting the eigenvalue counting function corresponding to the strictly positive eigenvalues of <i>A</i>_{<i>K</i>,,<i>m</i>}, we derive the bound <i>N</i>(, <i>A</i>_{<i>K</i>,,<i>m</i>}) (2<i></i>)^-<i>n</i><i></i>_n||{1 + [2<i>m</i>/(2<i>m</i> + <i>n</i>)]}^{<i>n</i>/(2<i>m</i>)}^{<i>n</i>/(2<i>m</i>)}, &gt; 0, where <i>_n</i> <i></i>^<i>n</i>/2 /((<i>n</i> + 2)/2) denotes the (Euclidean) volume of the unit ball in ^<i>n</i>.

The first two authors classified subfactor planar algebra generated by a non-trivial 2-box subject to the condition that the dimension of 3-boxes is at most 12 in Part I; 13 in Part II of this series. They are the group planar algebra for , the Fuss-Catalan planar algebra, and the group/subgroup planar algebra for Z_2 ⊂ Z_5 \rtimes Z_2.. In the present paper, we extend the classification to 14 dimensional 3-boxes. They are all Birman-Murakami-Wenzl algebras. Precisely it contains a depth 3 one from quantum O(3), and a one-parameter family from quantum S_p(4).