## Iterative solution of nonlinear equations involving set-valued uniformly accretive operators.(English)Zbl 1060.47511

Summary: Let $$E$$ be a real normed linear space and let $$A:E \mapsto 2^E$$ be a uniformly continuous and uniformly quasi-accretive multivalued map with nonempty closed values such that the range of $$(I-A)$$ is bounded and the inclusion $$f\in Ax$$ has a solution $$x^*\in E$$. It is proved that the Ishikawa and Mann type iteration processes converge strongly to $$x^*$$. Further, if $$T:E\mapsto 2^E$$ is a uniformly continuous and uniformly hemicontractive set-valued map with bounded range and a fixed point $$x^*\in E$$, it is proved that both the Mann and Ishikawa type iteration processes converge strongly to $$x^*$$. The strong convergence of these iteration processes with errors is also proved.

### MSC:

 47J25 Iterative procedures involving nonlinear operators 47H06 Nonlinear accretive operators, dissipative operators, etc. 65J15 Numerical solutions to equations with nonlinear operators 47H04 Set-valued operators
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### References:

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