Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Asymptotic behavior of nonexpansive sequences and mean points
HTML articles powered by AMS MathViewer

by Jong Soo Jung and Jong Seo Park PDF
Proc. Amer. Math. Soc. 124 (1996), 475-480 Request permission


Let $E$ be a real Banach space with norm $\Vert \cdot \Vert$ and let $\{x_n\}_{n \ge 0}$ be a nonexpansive sequence in $E$ (i.e., $\Vert x_{i + 1} - x_{j + 1}\Vert \le \Vert x_i - x_j\Vert$ for all $i, j \ge 0$). Let $K = \bigcap _{n = 1}^{\infty }\overline {co}\{\{x_i - x_{i - 1}\}_{i \ge n}\}$. We deal with the mean point of $\{\frac {x_n}{n}\}$ concerning a Banach limit. We show that if $E$ is reflexive and $d = d(0,K)$, then $d = d(0,\overline {co}\{\frac {x_n - x_0}{n}\})$ and there exists a unique point $z_0$ with $\Vert z_0\Vert = d$ such that $z_0 \in \overline {co}\{\frac {x_n - x_0}{n}\}$. This result is applied to obtain the weak and strong convergence of $\{\frac {x_n}{n}\}$.
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47H09
  • Retrieve articles in all journals with MSC (1991): 47H09
Additional Information
  • Jong Soo Jung
  • Affiliation: Department of Mathematics, Dong–A University, Pusan 604–714, Korea
  • Email:
  • Jong Seo Park
  • Affiliation: Department of Mathematics, Graduate School, Dong-A University, Pusan 604–714, Korea
  • Received by editor(s): March 24, 1994
  • Received by editor(s) in revised form: August 22, 1994
  • Additional Notes: This research was supported by the Korea Science and Engineering Foundation, project number 941-0100-035-2.
  • Communicated by: Palle E. T. Jorgensen
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 475-480
  • MSC (1991): Primary 47H09
  • DOI:
  • MathSciNet review: 1291776