Abstract:
In this paper, we develop the notion of (ψ, F)-contraction mappings introduced in [49] in b-metric
spaces. To achieve this, we introduce the notion of generalized multi-valued (ψ, S, F)-contraction
type I mapping with respect to generalized dynamic process D(S, T, x0), generalized multi-valued
(ψ, S, F)-contraction type II mapping with respect to generalized dynamic process D(S, T, x0), and
establish common fixed point results for these classes of mappings in complete b-metric spaces. As
an application, we obtain the existence of solutions of dynamic programming and integral equations.
The results presented in this paper extends and complements some related results in the literature.
