Boyd-Wong-type common fixed point results in cone metric spaces

Abstract

Some common fixed point results in cone metric spaces of C. Di Bari and P. Vetro [C. Di Bari, P. Vetro, phi-pairs and common fixed points in cone metric spaces, Rend. Cir. Mat. Palermo 57 (2008), 279-285] as well as P. Raja and S. M. Vaezpour [P. Raja, S. M. Vaezpour, Some extensions of Banach's Contraction Principle in complete metric spaces, Fixed Point Theory Appl. (2008), doi: 10.1155/2008/768294] are extended using generalized contractive-type conditions and cones which may be nonnormal. Cone metric versions of several well-known results, such as Boyd-Wong's theorem [D. W. Boyd, J.S. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969), 458-464], are obtained as special cases.