Abstract
In this paper, we introduce a new set F-s(b) of nonlinear functions. We obtain unique common fixed point theorems for (beta, F)-weak contractions under the effect of functions from F-s(b). Moreover, we deduce new common fixed point results in ordered and graphic b-metric spaces. Our work generalizes several recent results existing in the literature. We set up an example to elucidate main result. We apply the main theorem to show the existence of common solution of the system of elliptic boundary value problems.