Fixed point theorems for (ψ，Γ，α)-contractive mappings

To apply Γ function in fixed-point theory, two classes of ψ, Γ, α-contraction mappings on metric spaces are introduced． The properties of Γ function and fixed-point methods are used, to obtain certain fixed-point theorems, with an example given to support our conclusions． Our results answer questions for the existence of fixed-points for complex contraction mappings, but also improve and supplement existing results of function．