Fixed set of set valued mappings with set valued domain in terms of start set on a metric space with a graph

Fixexd point theory and applications

Binayak S Choudhury¹  Pradip Debnath²  Murchana Neog² 

[1] Department of Mathematics, Indian Institute of Engineering Science and Technology, Howrah, India;Department of Mathematics, North Eastern Regional Institute of Science and Technology, Nirjuli, India

关键词: fixed point;    fixed set;    start set;    set valued mapping;    metric space with a graph;    47H10;    54H25;    54E50;   

DOI  :  10.1186/s13663-017-0598-8

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this article, we define the new concept of a fixed set for a set valued map with set valued domain in the setting of metric space endowed with a directed graph. This notion of fixed set is analogous to the notion of a fixed point for a multivalued map and not for a classical single-valued map. We also introduce the new concept of the start set of a graph whose vertices are closed and bounded subsets of a metric space. Characterizations for such a graph to have a start set are given. Further, the notion of a self-path set valued map is defined and its relation with the start set is established. Finally, the existence of fixed sets is established in this context.

【 授权许可】

CC BY