Near Fixed Point Theorems in Hyperspaces

Near Fixed Point Theorems in Hyperspaces

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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, lovesense 3 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 here establish the so-called near fixed point theorems in Banach hyperspace.