N-Order Fixed Point Theory for N-Order Generalized Meir-Keeler Type Contraction in Partially Ordered Metric Spaces - Journal of Applied Mathematics and Physics

JAMP > Vol.7 No.5, May 2019

N-Order Fixed Point Theory for N-Order Generalized Meir-Keeler Type Contraction in Partially Ordered Metric Spaces ()

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DOI: 10.4236/jamp.2019.75078 714 Downloads 1,617 Views

Author(s)

Shiyun Wang^*, Jingwen Zhang

Affiliation(s)

Department of Science, Shenyang Aerospace University, Shenyang, China.

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.

KEYWORDS

Tripled Fixed Point, Meir-Keeler Type Contraction, Partially Ordered Set, N-Order Fixed Point

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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