Fixed points of mappings over a locally convex topological vector space and Ulam-Hyers stability of fixed point problems. (English) Zbl 1483.47087
Summary: This paper is dealt with the theory of fixed points of mappings which are an analogue like contraction mapping and Kannan mappings over a locally convex topological vector space. Some common fixed point theorems for a pair of mappings involving their iterates have been proved. The purpose of this paper is to examine the validity of established results on fixed points of contraction mappings and Kannan mappings over such a locally convex topological vector space. It is revealed that a suitable local base in locally convex topological vector space plays an important role to find fixed points of above mappings over it. Also an application relating to stability of fixed point equation for Kannan-type contractive mappings is obtained here.
MSC:
| 47H10 | Fixed-point theorems |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
Keywords:
locally convex topological vector space; contraction mapping; Kannan-type contractive mapping; \(T\)-contraction mapping; \(T\)-Kannan-type contractive mapping; uniformly convergent mapping; sequentially convergent mapping; subsequentially convergent mappingReferences:
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