Document Type : Research Paper

Authors

• Nahid Sadat Mohseni ¹
• Hashem P. Masiha ²
• Hamid Mamghaderi ²

¹ Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran.

² K. N. Toosi University of Technology

Abstract

In this paper, we discuss the existence of fixed points for Banach and Kannan contractions defined on $G$-metric spaces, which were introduced by Mustafa and Sims, endowed with a graph. Our results generalize and unify some recent results by Jachymski, Bojor and Mustafa and those contained therein. Moreover, we provide some examples to show that our results are substantial improvement of some known results in literature.

Keywords

• Fixed point
• $G$-metric spaces
• Banach contraction
• Kannan contraction