Abstract
In this paper, we use Suzuki-type contraction to prove three fixed point theorems for generalized contractions in an ordered space equipped with two metrics; we obtain some generalizations of the Kannan fixed point theorem. Our results on partially ordered metric spaces generalize and extend some results of Ran and Reurings as well as of Nieto and Rodríguez-López. To illustrate the effectiveness of our main result, we give an application to matrix equations which involves monotone mappings.
Highlights
1 Introduction It is well known that the Banach fixed point theorem plays a very important part in the resolution of various problems in nonlinear analysis such as integral equations and various nonlinear problems
In the same way we prove that lim n→+∞
We show that E(n) is closed for distance d
Summary
It is well known that the Banach fixed point theorem plays a very important part in the resolution of various problems in nonlinear analysis such as integral equations and various nonlinear problems. It has applications in various scientific disciplines. This theorem knew intense generalizations by the introduction of various type of contractions. We cite for example the generalizations obtained by Suzuki [20], Kikkawa and Suzuki [10], Mot and Petrusel [15], Dorić and Lazović [6], Bose and Roychowdhury [2], Singh, and Swami, Mishra, Chugh and Kamal [19]
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