On Some Common Fixed Point Theorems for Contractive Mappings

Various common fixed point theorems for self-mappings f, g on a metric space (X, d) satisfying some contractive conditions are known.It was shown in a previous paper [5] that certain contractive conditions can be reduced to the pairwise contractive condition (t)and those mappings which satisfy pairwise contractive conditions are studied in [5]-[7].However, in these earlier works, we mainly concerned with continuous mappings.The purpose of this paper is to offer, by relaxing slightly the pairwise contractive condition (t), a unified treatment of some common fixed point theorems for two self-mappings which satisfy certain contractive conditions but need not be continuous.The common fixed point theorems due to Fisher [l]-[3], Khan [9], Rhoades [11], and a fixed point theorem of Pal and Mai ti [ 1 0] wi 11 be derived from a common fixed point theorem (see Theorem 1 below) in L-spaces.Moreover, the author's results obtained in [8] will be also derived from a similar theorem (Theorem 2 below).