✦ LIBER ✦

Convergence Theorems for Continued Fractions in Banach Spaces

✍ Scribed by Andreas Schelling

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 390 KB
Volume: 86
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1996.0055

No coin nor oath required. For personal study only.

✦ Synopsis

Generalizations of S leszyn ski Pringheim's convergence criteria for ordinary continued fractions are proved for noncommutative continued fractions in Banach spaces. Some of them are exact generalizations of the scalar results.

📜 SIMILAR VOLUMES

Convergence Theorems for Best Approximat

Convergence Theorems for Best Approximations in a Nonreflexive Banach Space

✍ Jian-Hua Wang 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 225 KB

In this paper, we study continuity properties of the mapping P: (x, A) Ä P A (x) in a nonreflexive Banach space where P A is the metric projection onto A. Our results extend the existing convergence theorems on the best approximations in a reflexive Banach space to nonreflexive Banach spaces by usin

Convergence Conditions for Vector Stielt

Convergence Conditions for Vector Stieltjes Continued Fractions

✍ M.Castro Smirnova 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 142 KB

A Uniform Twin Parabola Convergence Theo

A Uniform Twin Parabola Convergence Theorem for Continued Fractions

✍ L.J. Lange 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 363 KB

On Osgood theorem in Banach spaces

✍ Stanislav Shkarin 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 165 KB 👁 1 views

## Abstract Let __X__ be a real Banach space, __ω__ : [0, +∞) → ℝ be an increasing continuous function such that __ω__(0) = 0 and __ω__(__t__ + __s__) ≤ __ω__(__t__) + __ω__(__s__) for all __t__, __s__ ∈ [0, +∞). According to the infinite dimensional analog of the Osgood theorem if ∫^1^~0~ (__ω__(_

Inverse and Implicit Function Theorems f

Inverse and Implicit Function Theorems for Nonsmooth Maps in Banach Spaces

✍ Zsolt Páles 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 273 KB

We extend the classical inverse and implicit function theorems, the implicit function theorems of Lyusternik and Graves, and the results of Clarke and Pourciau to the situation when the given function is not smooth, but it has a convex strict prederivative whose measure of noncompactness is smaller

The Banach-Steinhaus theorem for the spa

The Banach-Steinhaus theorem for the space (ℝ) in constructive analysis

✍ Satoru Yoshida 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 197 KB

## Abstract We prove the Banach‐Steinhaus theorem for distributions on the space 𝒟(ℝ) within Bishop's constructive mathematics. To this end, we investigate the constructive sequential completion $ \tilde {\cal D} $(ℝ) of 𝒟(ℝ).