Fixed point theory for generalized contractions in cone metric spaces

In this paper, we prove some fixed point theorems for generalized contractions in cone metric spaces. Our theorems extend some results of Suzuki (2008) [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc Amer Math Soc 136(5) (2008), 1861–1869] and Kikkawa and Suzuki (2008) [M. Kikkawa and T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal 69(9) (2008), 2942–2949].

Research highlights► Fixed point. ► Cone metric space. ► Hausdorff metric. ► Generalized contraction. ► Complete metric spaces.