New Versions of Some Results on Fixed Points in <i>b</i>-Metric Spaces

Abstract

The main and the most important objective of this paper is to nominate some new versions of several well-known results about fixed-point theorems such as Caristi’s theorem, Pant et al.’s theorem and Karapınar et al.’s theorem in the case of b-metric spaces. We use a new technique provided by Miculescu and Mihail in order to prove our theorems. Some illustrative applications and examples are given to strengthen our new findings and the main results.

Keywords

• iterative methods
• fixed point
• b-metric
• Caristi theorem
• orbitally continuous
• k-continuous