Abstract
In this paper, we introduce the concept of a c-comparison function with base s and utilized our new notion to establish some common fixed point theorems for nonlinear contractions in a complete b-metric space with base s in the sense of Czerwik[Czerwik S., Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Univ. Modena, 1998, 46, 263-276].