A note on some fundamental results in complete gauge spaces and application

Fixexd point theory and applications

Francesca Vetro¹  Bessem Samet²  Mohamed Jleli²  Calogero Vetro⁴ 

[1] degli Studi di Palermo, Palermo, Italy;Department of Mathematics, King Saud University, Riyadh, Saudi Arabia;Dipartimento Energia, Ingegneria dell’Dipartimento di Matematica e Informatica, UniversitàInformazione e Modelli Matematici (DEIM), Università

关键词: gauge structure;    fixed point;    monotone operator;    ordinary differential equation;    47H10;    54A20;    34L30;   

DOI  :  10.1186/s13663-015-0311-8

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We discuss the extension of some fundamental results in nonlinear analysis to the setting of gauge spaces. In particular, we establish Ekeland type and Caristi type results under suitable hypotheses for mappings and cyclic mappings. Our theorems generalize and complement some analogous results in the literature, also in the sense of ordered sets and oriented graphs. We apply our results to establishing the existence of solution to a second order nonlinear initial value problem.

【 授权许可】

CC BY