Minimization theorems and fixed point theorems in generating spaces of quasi-metric family

✍ Scribed by Gue Myung Lee; Byung Soo Lee; Jong Soo Jung; Shih-sen Chang

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 688 KB
• Volume: 101
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(97)00034-1

✦ Synopsis

By following the approaches of Kada et al. [13], we define a family of weak quasi-metrics in a generating space of quasimetric family. By using a family of weak quasi-metrics, we prove a Takahashi-type minimization theorem, a generalized Ekeland variational principle and a general Caristi-type fixed point theorem for set-valued maps in complete generating spaces of quasi-metric family. Also, by following the approach of Aubin [11], we prove another fixed point theorem for set-valued maps in complete generating spaces of quasi-metric family without the assumption of lower semicontinuity. From our results in complete generating spaces of quasi-metric family, we obtain the corresponding theorems for set-valued maps in complete fuzzy metric spaces. (~) 1999 Elsevier Science B.V. All rights reserved.