Document Type : Research Paper

Authors

• Wei-Shih Du ¹
• Th.M. Rassias ²

¹ Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan

² Department of Mathematics, National Technical University of Athens, Zofrafou Campus, 15780 Athens, Greece

Abstract

In this paper, we first establish a new fixed point theorem for a Meir-Keeler type condition. As an application, we derive a simultaneous generalization of Banach contraction principle, Kannan's fixed point theorem, Chatterjea's fixed point theorem and other fixed point theorems. Some new fixed point theorems are also obtained.

Keywords

• Simultaneous generalization
• Banach's type contraction
• Kannan's type contraction
• Chatterjea's type contraction
• Meir-Keeler's type contraction
• Banach contraction principle
• Kannan's fixed point theorem
• Chatterjea's fixed point theorem
• Meir-Keeler's fixed point theorem