Convergence theorems for generalized hemicontractive mapping in p-uniformly convex metric space. (English) Zbl 1476.54121
Summary: In this paper, we introduce and study an Ishikawa-type iteration process for the class of generalized hemicontractive mappings in \(p\)-uniformly convex metric spaces, and prove both \(\Delta\)-convergence and strong convergence theorems for approximating a fixed point of generalized hemicontractive mapping in complete \(p\)-uniformly convex metric spaces. We give a surprising example of this class of mapping that is not a hemicontractive mapping. Our results complement, extend and generalize numerous other recent results in CAT(0) spaces.
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54E40 | Special maps on metric spaces |
Keywords:
\(p\)-uniformly convex spaces; fixed point; hemicontractive mappings; generalized hemicontractive mappings; strong convergence; \( \Delta \)-convergenceReferences:
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