Nearly contraction mapping principle for fixed points of hemicontinuous mappings. (English) Zbl 1298.47067
Summary: We extend the application of nearly contraction mapping principle introduced by D. R. Sahu [Commentat. Math. Univ. Carol. 46, No. 4, 653–666 (2005; Zbl 1123.47041)] for existence of fixed points of demicontinuous mappings to certain hemicontinuous nearly Lipschitzian nonlinear mappings in Banach spaces. We have applied certain results due to Sahu [loc. cit.] to obtain conditions for existence – and to introduce an asymptotic iterative process for construction – of fixed points of these hemicontractions with respect to a new auxiliary operator.
MSC:
| 47H10 | Fixed-point theorems |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
Citations:
Zbl 1123.47041References:
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