Asymptotic behavior of generalized nonexpansive sequences and mean points

H. K. Pathak, D. O'regan, M. S. Khan, R. P. Agarwal

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Let E be a real Banach space with norm k-k and let fxngn, 0 be a generalized nonexpansive sequence in E (i.e. formula ommited where the series of nonnegative terms formula ommited is convergent). Let K = formula ommited We deal with the mean point of formula ommited concerning a Banach limit μ. If E is reflexive and d = d(0; K), then we show that formula ommited and there exists a pointformula ommited. In the sequel, this result is applied to obtain the weak and strong convergence of formula ommited.

Original languageEnglish
Pages (from-to)539-548
Number of pages10
JournalGeorgian Mathematical Journal
Volume11
Issue number3
DOIs
Publication statusPublished - Jan 1 2004

Fingerprint

Asymptotic Behavior
Banach Limit
Weak and Strong Convergence
Non-negative
Banach space
Norm
Series
Term

Keywords

  • Asymptotic behavior
  • Banach limit
  • generalized nonexpansive sequence
  • mean point
  • nonexpansive sequence

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Asymptotic behavior of generalized nonexpansive sequences and mean points. / Pathak, H. K.; O'regan, D.; Khan, M. S.; Agarwal, R. P.

In: Georgian Mathematical Journal, Vol. 11, No. 3, 01.01.2004, p. 539-548.

Research output: Contribution to journalArticle

Pathak, H. K. ; O'regan, D. ; Khan, M. S. ; Agarwal, R. P. / Asymptotic behavior of generalized nonexpansive sequences and mean points. In: Georgian Mathematical Journal. 2004 ; Vol. 11, No. 3. pp. 539-548.
@article{a98dd040372547f299428066c37e8a19,
title = "Asymptotic behavior of generalized nonexpansive sequences and mean points",
abstract = "Let E be a real Banach space with norm k-k and let fxngn, 0 be a generalized nonexpansive sequence in E (i.e. formula ommited where the series of nonnegative terms formula ommited is convergent). Let K = formula ommited We deal with the mean point of formula ommited concerning a Banach limit μ. If E is reflexive and d = d(0; K), then we show that formula ommited and there exists a pointformula ommited. In the sequel, this result is applied to obtain the weak and strong convergence of formula ommited.",
keywords = "Asymptotic behavior, Banach limit, generalized nonexpansive sequence, mean point, nonexpansive sequence",
author = "Pathak, {H. K.} and D. O'regan and Khan, {M. S.} and Agarwal, {R. P.}",
year = "2004",
month = "1",
day = "1",
doi = "10.1515/GMJ.2004.539",
language = "English",
volume = "11",
pages = "539--548",
journal = "Georgian Mathematical Journal",
issn = "1572-9176",
publisher = "Plenum Publishers",
number = "3",

}

TY - JOUR

T1 - Asymptotic behavior of generalized nonexpansive sequences and mean points

AU - Pathak, H. K.

AU - O'regan, D.

AU - Khan, M. S.

AU - Agarwal, R. P.

PY - 2004/1/1

Y1 - 2004/1/1

N2 - Let E be a real Banach space with norm k-k and let fxngn, 0 be a generalized nonexpansive sequence in E (i.e. formula ommited where the series of nonnegative terms formula ommited is convergent). Let K = formula ommited We deal with the mean point of formula ommited concerning a Banach limit μ. If E is reflexive and d = d(0; K), then we show that formula ommited and there exists a pointformula ommited. In the sequel, this result is applied to obtain the weak and strong convergence of formula ommited.

AB - Let E be a real Banach space with norm k-k and let fxngn, 0 be a generalized nonexpansive sequence in E (i.e. formula ommited where the series of nonnegative terms formula ommited is convergent). Let K = formula ommited We deal with the mean point of formula ommited concerning a Banach limit μ. If E is reflexive and d = d(0; K), then we show that formula ommited and there exists a pointformula ommited. In the sequel, this result is applied to obtain the weak and strong convergence of formula ommited.

KW - Asymptotic behavior

KW - Banach limit

KW - generalized nonexpansive sequence

KW - mean point

KW - nonexpansive sequence

UR - http://www.scopus.com/inward/record.url?scp=84896875327&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84896875327&partnerID=8YFLogxK

U2 - 10.1515/GMJ.2004.539

DO - 10.1515/GMJ.2004.539

M3 - Article

VL - 11

SP - 539

EP - 548

JO - Georgian Mathematical Journal

JF - Georgian Mathematical Journal

SN - 1572-9176

IS - 3

ER -