New concepts of f_{lambda,mu }-statistical convergence for double sequences of order α̃ and strong f_{lambda,mu }-Cesàro summability for double sequences of order α̃ are introduced for sequences of (complex or real) numbers. Furthermore, we give the relationship between the spaces w_{tilde{alpha },0}^{2} ( f,lambda,mu ), w_{tilde{alpha }}^{2} ( f,lambda,mu ) and w_{tilde{alpha},infty }^{2} ( f,lambda,mu ). Then we express the properties of strong f_{lambda,mu }-Cesàro summability of order β̃ which is related to strong f_{lambda,mu }-Cesàro summability of order α̃. Also, some relations between f_{lambda,mu }-statistical convergence of order α̃ and strong f_{lambda,mu }-Cesàro summability of order α̃ are given.