Higher-order Lipschitz mappings

Fixexd point theory and applications

Jeffery Ezearn¹ 

[1] Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

关键词: metric space;    fixed point;    Lipschitz mapping;    higher-order Lipschitz mapping;    local Lipschitzity;    stable and unstable polynomials;    Baire category theorem;    Perron-Frobenius theorem;    47H09;    47H10;   

DOI  :  10.1186/s13663-015-0334-1

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We study self-mappings on complete metric spaces, which we refer to as higher-order Lipschitz mappings. These mappings generalise Lipschitz mappings, the latter which are equivalent to first-order Lipschitz mappings studied in this paper. The main result of this paper is to extend the Banach fixed point theorem (and an often-cited generalisation) to higher-order contraction mappings. We also present results on the problem of local Lipschitzity of these higher-order Lipschitz mappings.

【 授权许可】

CC BY