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

作者：Jleli Mohamed; Samet Bessem^*; Vetro Calogero; Vetro Francesca

来源：Fixed Point Theory and Applications, 2015, 2015(1): 62.

DOI：10.1186/s13663-015-0311-8

• gauge structure
• fixed point
• monotone operator
• ordinary differential equation

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.

• 出版日期2015-4-29