Near Fixed Point Theorems in Hyperspaces

Hsien-Chung Wu
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Hsien-Chung Wu: Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan

Mathematics, 2018, vol. 6, issue 6, 1-15

Abstract: The hyperspace consists of all the subsets of a vector space. It is well-known that the hyperspace is not a vector space because it lacks the concept of inverse element. This also says that we cannot consider its normed structure, and some kinds of fixed point theorems cannot be established in this space. In this paper, we shall propose the concept of null set that will be used to endow a norm to the hyperspace. This normed hyperspace is clearly not a conventional normed space. Based on this norm, the concept of Cauchy sequence can be similarly defined. In addition, a Banach hyperspace can be defined according to the concept of Cauchy sequence. The main aim of this paper is to study and establish the so-called near fixed point theorems in Banach hyperspace.

Keywords: Cauchy sequence; near fixed point; Banach hyperspace; normed hyperspace; null set (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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