Common fixed point results for four maps satisfying contractive condition in multiplicative b-metric spaces

Abstract

In this paper, we discuss the unique common fixed point of two pair of weakly compatible mappings on a complete multiplicative b-metric space, which satisfies the following inequality:
d(Sx,Ty)≤[k{max{d(Ax,By),d(Ax,Sx),d(By,Ty),d(Sx,By),d(Ax,Ty)}}]λ,
where A and S are weakly compatible, B and T also are weakly compatible. Our results improve and generalize the results of X. He et al. [3].