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Boyd-Wong-type common fixed point results in cone metric spaces. (English) Zbl 1213.54059
Summary: Some common fixed point results in cone metric spaces of C. Di Bari and P. Vetro [Rend. Circ. Mat. Palermo (2) 57, No. 2, 279–285 (2008; Zbl 1164.54031)] as well as P. Raja and S. M. Vaezpour [Fixed Point Theory Appl. 2008, Article ID 768294 (2008; Zbl 1148.54339)] 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 and J. S. W. Wong, Proc. Amer. Math. Soc. 20, 458–464 (1969; Zbl 0175.44903)], are obtained as special cases.
MSC:
54H25Fixed-point and coincidence theorems in topological spaces
47H10Fixed point theorems for nonlinear operators on topological linear spaces
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