In this paper, we introduce frames generated by double sequences (d-frame) in Hilbert spaces and describe some of their properties. Furthermore, discuss frame operators, alternate dual stability for d-frames.

In earlier works, F. León and coworkers discovered a remarkable structure between statistical convergence strong Cesàro convergence, modulated by function f (called modulus function). Such nice pivots around the notion of compatible function. this paper, we will explore such in framework lacunary for double sequences discover that remains true functions. Thus, continue work Hacer Şenül, Mikail ...