On fixed point theorems for monotone increasing vector valued mappings via scalarizing. (English) Zbl 1319.47047
Summary: In this paper, first we prove some lemma, then by using the nonlinear scalarization mapping, we present some fixed point theorems for a vector valued mapping. The main result obtained can be viewed as an extension, improvement and repairment of the main theorem given in [V. Kostrykin and A. Oleynik, Fixed Point Theory Appl. 2012, Article ID 211, 4 p., electronic only (2012; Zbl 1320.47051)].
MSC:
| 47H10 | Fixed-point theorems |
| 47H07 | Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces |
| 46B40 | Ordered normed spaces |
Keywords:
fixed point; nonlinear scalarization mapping; solid cone; minihedral cone; vector valued mapping; partially ordered normed vector spaceCitations:
Zbl 1320.47051References:
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