N-Order Fixed Point Theory for N-Order Generalized Meir-Keeler Type Contraction in Partially Ordered Metric Spaces ()
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.
Share and Cite:
Wang, S. and Zhang, J. (2019)
N-Order Fixed Point Theory for N-Order Generalized Meir-Keeler Type Contraction in Partially Ordered Metric Spaces.
Journal of Applied Mathematics and Physics,
7, 1174-1184. doi:
10.4236/jamp.2019.75078.
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