Stability results and qualitative properties for Mann’s algorithm via admissible perturbations technique

In this paper we will present data dependence results for Mann iteration schene related to the fixed point inclusion.

The approach is based on the admissible perturbation method introduced by A. Petrusel and I.A. Rus. Then, we exemplify this approach for the case of multi-valued contractions defined on a metric space endowed with a convexity structure in the sense of Takahashi.

Moreover, we will present some qualitative properties of the fixed point problem for multi-valued contractions involving Mann iteration, such as: Ulam-Hyers stability, T-stability and well-posedness of the fixed point problem.

Cristian-Daniel Alecsa
Babes-Bolyai University, Department of Mathematics, Cluj-Napoca, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania

Fixed point problem; multi-valued contractions; data dependence; iterative algorithm; Ulam-Hyers stability; well-possedness

See the expanding block below.

C.D. Alecsa, Stability results and qualitative properties for Mann’s algorithm via admissible perturbations technique, Applied Analysis and Optimization, 1 (2017) no. 2, 327-344.

http://www.ybook.co.jp/online-p/AAO/vol1/aaov1n2p327.pdf

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