COMMON FIXED POINT THEOREMS FOR TWO SELFMAPPINGS OF A b-METRIC SPACE UNDER AN IMPLICIT RELATION

In the setting of a b-metric space (see Stefan Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis 1, 5–11, 1993 and Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena 46 (2), 263–276, 1998), we establish a general common fixed point theorem for two weakly compatible selfmappings satisfying the (E.A) condition (see M. Aamri and D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, Math. Anal. Appl. 270, 181-188, 2002) under a contractive condition using a class of implicit relations.