Near fixed point theorems in near Banach spaces

The near vector space in which the additive inverse element does not necessarily exist is introduced in this paper. The reason is that an element in a near vector space which subtracts itself may not be a zero element. Therefore, the concept of a null set is introduced in this paper to play the role of a zero element. A near vector space can also be endowed with a norm to define a so-called near normed space. Based on this norm, the concept of a Cauchy sequence can be similarly defined. A near Banach space can also be defined according to the concept of completeness using the Cauchy sequences. The main aim of this paper is to establish the so-called near fixed point theorems and Meir-Keeler type of near fixed point theorems in near Banach spaces.