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

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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

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10.1016/j.top.2009.11.017

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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",

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AU - Prykarpatsky, Anatoliy K.

AU - Blackmore, Denis

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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

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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

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