Abstract:
In this paper, we derive some fixed point theorems in the projective tensor product (X⨂γ Y) of two Banach spaces X and Y. Using two mappings T1: X⨂γ Y->Y and we construct a self-mapping T on X⨂γ Y. Taking T1and T2 as different contractive type mappings, we study the characteristics of the mapping T and the existence and the uniqueness of the fixed point of T in the closed unit ball of X⨂γ Y. The converse of this result is also discussed here.
Keywords: Projective tensor product, contractive type mappings, asymptotically regular property