Abstract
Let K be a closed convex subset of a real Hilbert space H and let T:K→K be a continuous pseudocontractive mapping. Then for βε(0,1) and each tε(0,1), there exists a sequence { yt}⊂K satisfying yt=βPK[(1-t)yt]+(1-β)T(yt) which converges strongly, as t→0+, to the minimum-norm fixed point of T. Moreover, we provide an explicit iteration process which converges strongly to a minimum-norm fixed point of T provided that T is Lipschitz. Applications are also included. Our theorems improve several results in this direction.
| Original language | English |
|---|---|
| Article number | 926017 |
| Journal | Abstract and Applied Analysis |
| Volume | 2012 |
| DOIs | |
| Publication status | Published - Dec 1 2012 |
All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
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Cite this
Zegeye, H., Shahzad, N., & Alghamdi, M. A. (2012). Minimum-norm fixed point of pseudocontractive mappings. Abstract and Applied Analysis, 2012, [926017]. https://doi.org/10.1155/2012/926017