Remarks on Caristi’s fixed point theorem and Kirk’s problem

✍ Scribed by Zhilong Li

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 238 KB
• Volume: 73
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2010.07.048

✦ Synopsis

Without assumptions on the continuity and the subadditivity of η, by means of Caristi's fixed point theorem, we investigated the existence of fixed points for a Caristi type mapping which partially answered Kirk's problem and improved Caristi's fixed point theorem, Jachymski's fixed point theorem and Khamsi's fixed point theorem since ϕ is not necessarily assumed to be bounded below on X .