Generalizations of fixed point theorems and computation

Qing Xu; Chuangyin Dang; Daoli Zhu

doi:10.1016/j.jmaa.2009.01.020

Generalizations of fixed point theorems and computation

Qing Xu
, Chuangyin Dang
, Daoli Zhu

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

3 Citations (Scopus)

Abstract

As a powerful mechanism, fixed point theorems have many applications in mathematical and economic analysis. In this paper, the well-known Brouwer fixed point theorem and Kakutani fixed point theorem are generalized to a class of nonconvex sets and a globally convergent homotopy method is developed for computing fixed points on this class of nonconvex sets. Crown Copyright © 2009.

Original language	English
Pages (from-to)	550-557
Journal	Journal of Mathematical Analysis and Applications
Volume	354
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2009.01.020
Publication status	Published - 15 Jun 2009

Research Keywords

Fixed point
Global convergence
Homotopy method
Nonconvex set

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title = "Generalizations of fixed point theorems and computation",

abstract = "As a powerful mechanism, fixed point theorems have many applications in mathematical and economic analysis. In this paper, the well-known Brouwer fixed point theorem and Kakutani fixed point theorem are generalized to a class of nonconvex sets and a globally convergent homotopy method is developed for computing fixed points on this class of nonconvex sets. Crown Copyright {\textcopyright} 2009.",

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author = "Qing Xu and Chuangyin Dang and Daoli Zhu",

year = "2009",

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TY - JOUR

T1 - Generalizations of fixed point theorems and computation

AU - Xu, Qing

AU - Dang, Chuangyin

AU - Zhu, Daoli

PY - 2009/6/15

Y1 - 2009/6/15

N2 - As a powerful mechanism, fixed point theorems have many applications in mathematical and economic analysis. In this paper, the well-known Brouwer fixed point theorem and Kakutani fixed point theorem are generalized to a class of nonconvex sets and a globally convergent homotopy method is developed for computing fixed points on this class of nonconvex sets. Crown Copyright © 2009.

AB - As a powerful mechanism, fixed point theorems have many applications in mathematical and economic analysis. In this paper, the well-known Brouwer fixed point theorem and Kakutani fixed point theorem are generalized to a class of nonconvex sets and a globally convergent homotopy method is developed for computing fixed points on this class of nonconvex sets. Crown Copyright © 2009.

KW - Fixed point

KW - Global convergence

KW - Homotopy method

KW - Nonconvex set

UR - https://www.scopus.com/pages/publications/60349121419

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-60349121419&origin=recordpage

U2 - 10.1016/j.jmaa.2009.01.020

DO - 10.1016/j.jmaa.2009.01.020

M3 - RGC 21 - Publication in refereed journal

SN - 0022-247X

VL - 354

SP - 550

EP - 557

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Generalizations of fixed point theorems and computation

Abstract

Research Keywords

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