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On \(T\)-stability of Picard iteration in cone metric spaces. (English) Zbl 1202.54030

Summary: The aim of this work is to investigate the \(T\)-stability of Picard’s iteration procedures in cone metric spaces and give an application.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
47J25 Iterative procedures involving nonlinear operators
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References:

[1] Huang L-G, Zhang X: Cone metric spaces and fixed point theorems of contractive mappings.Journal of Mathematical Analysis and Applications 2007,332(2):1468-1476. 10.1016/j.jmaa.2005.03.087 · Zbl 1118.54022 · doi:10.1016/j.jmaa.2005.03.087
[2] Zhiqun, X., Remarks of equivalence among Picard, Mann, and Ishikawa iterations in normed spaces, 5 (2007) · Zbl 1155.47316
[3] Vasilev FP: Numerical Methodes for Solving Extremal Problems. 2nd edition. Nauka, Moscow, Russian; 1988:550.
[4] Harder AM, Hicks TL: Stability results for fixed point iteration procedures.Mathematica Japonica 1988,33(5):693-706. · Zbl 0655.47045
[5] Qing, Y.; Rhoades, BE, [InlineEquation not available: see fulltext.]-stability of Picard iteration in metric spaces, 4 (2008)
[6] Ilic D, Rakocevic V: Quasi-contraction on a cone metric space.Applied Mathematics Letters 2009,22(5):728-731. 10.1016/j.aml.2008.08.011 · Zbl 1179.54060 · doi:10.1016/j.aml.2008.08.011
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