✦ LIBER ✦

The existence of a weighted mean for almost periodic functions

✍ Scribed by Toka Diagana

Publisher: Elsevier Science
Year: 2011
Tongue: English
Weight: 202 KB
Volume: 74
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2011.04.008

No coin nor oath required. For personal study only.

✦ Synopsis

In a recent paper by Liang et al. (2010) [1], the original question which is that of the existence of a weighted mean for almost periodic functions was raised. In particular, they showed through an example that there exist weights for which a weighted mean for almost periodic functions may or may not exist. In this note we give some sufficient conditions which do guarantee the existence of a weighted mean for almost periodic functions, which will then coincide with the classical Bohr mean. Moreover, we will show that under those conditions, the corresponding weighted Bohr transform exists.

📜 SIMILAR VOLUMES

On the existence of almost periodic comp

On the existence of almost periodic complete trajectories for contractive almost periodic processes

✍ Hitoshi Ishii 📂 Article 📅 1982 🏛 Elsevier Science 🌐 English ⚖ 383 KB

A Compactness Criterion for the Space of

A Compactness Criterion for the Space of Almost Periodic Functions

✍ F. Jeschek; H. Poppe; A. Stärk 📂 Article 📅 1977 🏛 John Wiley and Sons 🌐 English ⚖ 165 KB

A compactness criterion for the space of

A compactness criterion for the space of almost periodic functions, II

✍ H. Poppe; A. Stärk 📂 Article 📅 1982 🏛 John Wiley and Sons 🌐 English ⚖ 225 KB

On the existence of periodic solutions a

On the existence of periodic solutions and almost periodic solutions for nonlinear systems

✍ Shigeo Kato; Masato Imai 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 369 KB

The existence of almost periodic solutio

The existence of almost periodic solutions of a certain nonlinear system

✍ Yuanheng Wang; Yong-Hui Xia 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 302 KB

This paper studies a certain nonlinear system. By averaging method and exponential dichotomy, some sufficient conditions are given for the existence of almost periodic solutions of the system. The results generalize the known ones.

Existence of a positive almost periodic

Existence of a positive almost periodic solution for a nonlinear delay integral equation

✍ Bin Xu; Qingye Zhang 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 219 KB

In this paper, we discuss the existence of positive almost periodic solution for some nonlinear delay integral equation, by constructing a new fixed point theorem in the cone. Some known results are extended.