Some fixed point theorems in 2-Banach spaces
by
Shyam Patkar
Truba Institute of Engg. and Information Technology Bhopal,INDIA
Coauthors: Ramakant Bhardwaj

There are several generalizations of classical contraction mapping theorem of Banach. In a paper Gahler [1] defined a linear 2-narmed space to be pair (L, ||., || ) where L is a Linear space and ||., . || is non negative, real valued function defined on L such that

a, b, c, L

(1.1) || a, b || = 0 if and only if a and b are linearly dependent

(1.2) || a, b || = || b, a ||

(1.3) || a, b || = || || a, b || ,  is real

(1.4) || a, b+c ||  || a, b || +|| a, c ||

Hence ||., . || is called a 2-narm.

Our object in this paper is to prove some fixed point and common Fixed-point theorems using two Banach Space.

Keywords: Fixed point ,Banach Spaces,2-Banach Spaces .

Date received: May 1, 2008