Convergence of perturbed iterates of set-valued mappings

We continue our study of the existence of convergent iterations in the presence of computational errors for a nonexpansive setvalued mapping. In a recent paper we have shown that if for any initial point, there exists a trajectory of a nonexpansive set-valued mapping attracted by a given set, then this property is stable under small perturbations of the mapping. In particular, we have shown there that for any initial point, there exists a trajectory with a subsequence which is attracted by the attractor. In the present paper we show, under certain mild additional assumptions, that for any initial point, there exists a trajectory such that, for any given positive e\epsilon, almost all of its elements belong to an e\epsilon-neighborhood of the attractor.     

Three Generic Results in Holomorphic Fixed Point Theory

We establish three theorems which show that most of the bounded holomorphic self-mappings of a star-shaped domain in a complex Banach space map it strictly inside itself. According to the Earle–Hamilton fixed point theorem, each such mapping has a unique fixed point.     

A projection method for solving nonlinear problems in reflexive Banach spaces

We study the convergence of an iterative algorithm for finding common fixed points of finitely many Bregman firmly nonexpansive operators in reflexive Banach spaces. Our algorithm is based on the concept of the so-called shrinking projection method and it takes into account possible computational errors. We establish a strong convergence theorem and then apply it to the solution of convex feasibility and equilibrium problems, and to finding zeroes of two different classes of nonlinear mappings.     

Synthesis and characterization of fast-decaying bluish green phosphors of Tb3+-doped CaSi2O2N2 for 2D/3D plasma display panels

Oxynitride phosphor powders comprising of CaSi₂O₂N₂ doped with Tb³⁺ were successfully synthesized using a high-temperature solid-state reaction method. The experimentally determined photoluminescence (PL) properties of the produced phosphors meet the requirements of 2D/3D plasma display panels (PDPs). In particular, under the excitation of vacuum ultraviolet (VUV) synchrotron radiation and ultraviolet (UV) irradiation, emission peaks corresponding to the ⁵D₃→⁷F_J (J=6, 5, 4, 3) and ⁵D₄→⁷F_J (J=6, 5, 4, 3) transitions of Tb³⁺ ions were recorded. Monitoring the ⁵D₄→⁷F₅ emission of Tb³⁺ at 545 nm, the excitation bands were assigned to the host-related absorption as well as the 4f–5d (fd) and the 4f–4f (ff) transitions of Tb³⁺. The produced phosphors can be efficiently excited at 147 nm, and have an adequately short decay time (τ_1/10=1.14 ms).     

A convergence theorem for asymptotic contractions

We show that to each asymptotic contraction T with a bounded orbit in a complete metric space X, there corresponds a unique point x _* such that all the iterates of T converge to x _*, uniformly on any bounded subset of X. If, in addition, some power of T is continuous at x _*, then x _* is a fixed point of T. Dedicated to Professor Felix E. Browder with admiration and respect     

Affine blocking sets, three-dimensional codes and the Griesmer bound

We construct families of three-dimensional linear codes that attain the Griesmer bound and give a non-explicit construction of linear codes that are one away from the Griesmer bound. All these codes contain the all-1 codeword and are constructed from small multiple blocking sets in AG(2,q).     

Theorems of Denjoy–Wolff type

Using the Kobayashi distance, we first establish a version of the Denjoy–Wolff theorem for a bounded and strictly convex domain in ${{\mathbb{C}}^k}$ . Next, we prove analogous results for semigroups of holomorphic mappings and the resolvents of their generators. Finally, we obtain theorems of Denjoy–Wolff type for families of holomorphic retracts of the open unit ball in a complex, reflexive, and strictly convex Banach space.