A solution set analysis of a nonlinear operator equation using a Leray-Schauder type fixed point approach

Anatoliy K. Prykarpatsky; Denis Blackmore

doi:10.1016/j.top.2009.11.017

A solution set analysis of a nonlinear operator equation using a Leray-Schauder type fixed point approach

Anatoliy K. Prykarpatsky, Denis Blackmore

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Here we study the solution set of a nonlinear operator equation in a Banach subspace Lⁿ ⊂ C (X) by reducing it to a Leray-Schauder type fixed point problem. The subspace Lⁿ is of finite codimension n ∈ Z₊ in C (X), with X an infinite compact Hausdorff space, and is defined by conditions α_i^* (f) {colon equals} ∫_X f (x) d μ_i (x) = 0, f ∈ C (X), with norms {norm of matrix} μ_i {norm of matrix} = 1, i = 1, ..., n.

Original language	English (US)
Pages (from-to)	182-185
Number of pages	4
Journal	Topology
Volume	48
Issue number	2-4
DOIs	https://doi.org/10.1016/j.top.2009.11.017
State	Published - Jun 2009

All Science Journal Classification (ASJC) codes

Geometry and Topology

Keywords

Fixed point theory
Leray-Schauder type theorem
Nonlinear operator equation
Solution set analysis

Access to Document

10.1016/j.top.2009.11.017

Cite this

@article{4b8359aa78994a00b90c568368eba2a0,

title = "A solution set analysis of a nonlinear operator equation using a Leray-Schauder type fixed point approach",

abstract = "Here we study the solution set of a nonlinear operator equation in a Banach subspace Ln ⊂ C (X) by reducing it to a Leray-Schauder type fixed point problem. The subspace Ln is of finite codimension n ∈ Z+ in C (X), with X an infinite compact Hausdorff space, and is defined by conditions αi* (f) \{colon equals\} ∫X f (x) d μi (x) = 0, f ∈ C (X), with norms \{norm of matrix\} μi \{norm of matrix\} = 1, i = 1, ..., n.",

keywords = "Fixed point theory, Leray-Schauder type theorem, Nonlinear operator equation, Solution set analysis",

author = "Prykarpatsky, \{Anatoliy K.\} and Denis Blackmore",

year = "2009",

month = jun,

doi = "10.1016/j.top.2009.11.017",

language = "English (US)",

volume = "48",

pages = "182--185",

journal = "Topology",

issn = "0040-9383",

publisher = "Elsevier Ltd",

number = "2-4",

}

TY - JOUR

T1 - A solution set analysis of a nonlinear operator equation using a Leray-Schauder type fixed point approach

AU - Prykarpatsky, Anatoliy K.

AU - Blackmore, Denis

PY - 2009/6

Y1 - 2009/6

N2 - Here we study the solution set of a nonlinear operator equation in a Banach subspace Ln ⊂ C (X) by reducing it to a Leray-Schauder type fixed point problem. The subspace Ln is of finite codimension n ∈ Z+ in C (X), with X an infinite compact Hausdorff space, and is defined by conditions αi* (f) {colon equals} ∫X f (x) d μi (x) = 0, f ∈ C (X), with norms {norm of matrix} μi {norm of matrix} = 1, i = 1, ..., n.

AB - Here we study the solution set of a nonlinear operator equation in a Banach subspace Ln ⊂ C (X) by reducing it to a Leray-Schauder type fixed point problem. The subspace Ln is of finite codimension n ∈ Z+ in C (X), with X an infinite compact Hausdorff space, and is defined by conditions αi* (f) {colon equals} ∫X f (x) d μi (x) = 0, f ∈ C (X), with norms {norm of matrix} μi {norm of matrix} = 1, i = 1, ..., n.

KW - Fixed point theory

KW - Leray-Schauder type theorem

KW - Nonlinear operator equation

KW - Solution set analysis

UR - https://www.scopus.com/pages/publications/77549088366

UR - https://www.scopus.com/inward/citedby.url?scp=77549088366&partnerID=8YFLogxK

U2 - 10.1016/j.top.2009.11.017

DO - 10.1016/j.top.2009.11.017

M3 - Article

AN - SCOPUS:77549088366

SN - 0040-9383

VL - 48

SP - 182

EP - 185

JO - Topology

JF - Topology

IS - 2-4

ER -

A solution set analysis of a nonlinear operator equation using a Leray-Schauder type fixed point approach

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this