TITLE:
N-Order Fixed Point Theory for N-Order Generalized Meir-Keeler Type Contraction in Partially Ordered Metric Spaces
AUTHORS:
Shiyun Wang, Jingwen Zhang
KEYWORDS:
Tripled Fixed Point, Meir-Keeler Type Contraction, Partially Ordered Set, N-Order Fixed Point
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.5,
May
29,
2019
ABSTRACT: This paper concerns N-order fixed point theory in partially
ordered metric spaces. For the sake of simplicity, we start our investigations
with the tripled case. We define tripled generalized Meir-Keeler type
contraction which extends the definition of [Bessem Samet, Coupled fixed point
theorems for a generalized Meir-Keeler contraction in partially ordered metric
spaces, Nonlinear Anal. 72 (2010), 4508-4517]. We then discuss the existence
and uniqueness of tripled fixed point theorems in partially ordered metric
spaces. For general cases, we generalized our results to the N-order case. The results will promote
the study of N-order fixed point
theory.