Some fixed point theorems in 2-Banach spaces and 2-normed tensor product spaces

In this paper, we derive some fixed point theorems in 2-Banach spaces. Let X be a 2-Banach space and T be a self-mapping on X. Let psi: [0,infty) to [0,infty) ; beta,phi: [0,infty)times [0,infty) to [0,infty) and gamma :[0,infty)times [0,infty)times [0,infty) to [0,infty) be continuous mappings having some specific characteristics. Using these mappings, we define some conditions for T under which T has a unique fixed point in X. The conditions for two self-mappings T1 and T2 on X for having the common unique fixed point are also derived here with proper examples. Moreover, defining a 2-norm in the projective tensor product space, we derive a fixed point theorem here with a suitable example.