Data Dependence for Ishikawa Iteration When Dealing with Contractive-Like Operators

By Şm Şoltuz, Teodor Grosan. 2008

146 citations recorded by the source corpus.

We prove a convergence result and a data dependence for Ishikawa iteration when applied to contraction-like operators. An example is given, in which instead of computing the fixed point of an operator, we approximate the operator with a contractive-like one. For which it is possible to compute the fixed point, and therefore to approximate the fixed point of the initial operator.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/1473d0554270a07015d1e662883a20c80777e6eb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Vatan Karakaya
2. Faik Gursoy
3. B. Rhoades

In Geometry and Topology

1. Vatan Karakaya
2. Faik Gursoy
3. B. Rhoades
4. Mujahid Abbas
5. Stojan Radenovic
6. E. Karapınar
7. Zoran Kadelburg
8. Muhammad Arshad

In Numerical Analysis

1. Vatan Karakaya
2. Faik Gursoy
3. B. Rhoades
4. Muhammad Arshad
5. Kifayat Ullah

Citations in the corpus

• A PICARD-S HYBRID TYPE ITERATION METHOD FOR SOLVING A DIFFERENTIAL EQUATION WITH RETARDED ARGUMENT (2014, background): “[41] Let {βn}∞n=0 be a nonnegative sequence for which one assumes there exists n0 ∈ N, such that for all n ≥ n0 one has satisfied the inequality”
• SOME FIXED POINT RESULTS FOR A NEW THREE STEPS ITERATION PROCESS IN BANACH SPACES (2017, background): “[18] Let {an}n=1 be a nonnegative real sequence and there exists n0 ∈ N such that for all n ≥ n0 satisfying the following condition: an+1 ≤ (1− μn)an + μnηn, (1.”
• Data dependence results of new multi-step and S-iterative schemes for contractive-like operators (2012, methodology): “Several authors who have made contributions to the study of data dependence of fixed points are Rus and Muresan [12], Rus et al. [13, 14], Berinde [36], Esṕınola and Petruşel [22], Markin [16], Chifu and Petruşel [5], Olantiwo [18, 19], Şoltuz [30, 31], Şoltuz and Grosan [32], Chugh and Kumar [”