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.
|Number of pages||13|
|Journal||Fixed Point Theory and Applications|
|Publication status||Published - 2015|
All Science Journal Classification (ASJC) codes
- Geometry and Topology
- Applied Mathematics
Vetro, F., Vetro, C., Jleli, M., Vetro, F., Vetro, C., & Samet, B. (2015). A note on some fundamental results in complete gauge spaces and application. Fixed Point Theory and Applications, 2015, 1-13.