continuity and fixed point of a new extension of f-suzuki-contraction mappings in b-metric spaces with application

In this paper, firstly, we introduce a new extension of f-suzuki-contrac-tion map-pings namely generalized fp-suzuki contraction. moreover, we prove a fixed point theorem for such contraction mappings even without considering the completeness condition of space. in the following, we respond the open question of rhoades(see rhoades [26], p.242) regarding existence of a contractive definition which is strong enough to generate a fixed point but dose not force the mapping to be continuous at the fixed point. also, we provide some examples show that our main theorem is a generalization of previous results. finally, we give an application to the boundary value problem of a nonlinear fractional differential equation for our results.