Answers to questions on Kannan's fixed point theorem in strong b-metric spaces

Abstract

Our purpose of this paper is to answer several open questions posed by Doan (AIMS Math., 6 (2021), 7895–7908). First, we present two fixed point theorems, which are positive answers to Doan's questions. Second, we establish a new type of Riech's fixed point theorem to improve a result of Doan. Finally, we offer a straightforward example illustrating that a set-valued mapping satisfying the conditions of our fixed point theorem may has more than one fixed point.

Keywords

• fixed point
• strong $ b $-metric space
• geraghty functions
• kannan mapping
• riech's fixed point theorem
• multi-valued mapping