On the existence of non-linear frames
A stronger version of the notion of frame in Banach space called Strong Retro Banach frame (SRBF) is defined and studied. It has been proved that if is a Banach space such that has a SRBF, then has a Bi-Banach frame with some geometric property. Also, it has been proved that if a Banach space has an approximative Schauder frame, then has a SRBF. Finally, the existence of a non-linear SRBF in the conjugate of a separable Banach space has been proved.