Fixed point theory for a new type of contractive multivalued operators

The aim of this paper is to discuss some basic problems (data dependence, well-posedness, nonself operators, homotopy results, generalized contractions) of the fixed point theory for a new type contractive multivalued operator. The results complement and extend some very recent results proved by M. Kikkawa and T. Suzuki, as well as, other theorems given by M. Frigon and A. Granas, S. Reich, I.A. Rus, etc.