Common Fixed Point Theorems in Dislocated Cone Metric Spaces

Jungck and Rhoades [20] introduced the notion of weakly compatible mappings, which is weaker than compatibility. Many interesting fixed point theorems for weakly compatible maps satisfying contractive type conditions have been obtained by various authors. In this paper, notion of dislocated cone is introduced and a common fixed point theorem for three pairs of weakly compatible mappings satisfying a rational inequality without any continuity requirement which generalize several previously known results due to Imdad and Ali [15], Goyal ([6], [7]), Goyal and Gupta ([8], [9]), Imdad-Khan [16], Jeong-Rhoades [17] and others. 2010 Mathematical Sciences Classification: 54H25, 47H10