Fixed point theory in cone metric spaces obtained via the scalarization method. (English) Zbl 1197.54055

Amini-Harandi, A.; Fakhar, M.

Comput. Math. Appl. 59, No. 11, 3529-3534 (2010).

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:

54H25	Fixed-point and coincidence theorems (topological aspects)
65J15	Numerical solutions to equations with nonlinear operators
47H10	Fixed-point theorems

Keywords:

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

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