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Zbl 1197.54055
Amini-Harandi, A.; Fakhar, M.
Fixed point theory in cone metric spaces obtained via the scalarization method. (English)
[J] Comput. Math. Appl. 59, No. 11, 3529-3534 (2010). ISSN 0898-1221

Summary: Motivated by the scalarization method in vector optimization theory, we take a new approach to fixed point theory on cone metric spaces. By using our method, we prove some fixed point theorems and several common fixed point theorems on cone metric spaces in which the cone need not be normal. Our results improve and generalize many well-known results from the literature.
MSC 2000:
*54H25 Fixed-point theorems in topological spaces
65J15 Equations with nonlinear operators (numerical methods)
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: fixed point; cone metric space; ordered Banach space; scalarization method

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