TITLE:
A General Method of Researching the N-Ordered Fixed Point on a Metric Space with a Graph
AUTHORS:
Xiaonan Liang, Shiyun Wang
KEYWORDS:
N-Order Fixed Point, Product Metric Space Endowed with a Graph, Set-Valued Mapping, SG-Contraction
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.8 No.12,
December
17,
2020
ABSTRACT: In this paper, we propose a new perspective to discuss the N-order fixed point theory of set-valued and single-valued mappings. There are two aspects in our work: we first define a product metric space with a graph for the single-valued mapping whose conversion makes the results and proofs concise and straightforward, and then we propose an SG-contraction definition for set-valued mapping which is more general than some recent contraction’s definition. The results obtained in this paper extend and unify some recent results of other authors. Our method to discuss the N-order fixed point unifies N-order fixed point theory of set-valued and single-valued mappings.