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Start Over Author "ZHIQUN XUE" Journal fixed point theory and applications
7 results on '"ZHIQUN XUE"'

3. The Comparison of the Convergence Speed between Picard, Mann, Krasnoselskij and Ishikawa Iterations in Banach Spaces

Author

Zhiqun Xue

Subjects
Applied mathematics. Quantitative methods, T57-57.97, Analysis, QA299.6-433
Abstract

The purpose of this paper is to compare convergence speed of the Picard and Mann iterations on one hand, Krasnoselskij and Ishikawa iterations on the other hand, for the class of Zamfirescu operators. The results improve corresponding results of (Berinde 2004) and (Babu and Vara Prasad 2006).

Published
2008
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5. On Equivalence of Some Iterations Convergence for Quasi-Contraction Maps in Convex Metric Spaces

Author

Guiwen Lv, Zhiqun Xue, and Billy E. Rhoades

Subjects
Discrete mathematics, T57-57.97, QA299.6-433, Applied mathematics. Quantitative methods, Applied Mathematics, Equivalence of metrics, Convex metric space, Mathematics::Algebraic Geometry, Differential geometry, Geometry and Topology, Equivalence (formal languages), Contraction (operator theory), Analysis, Mathematics
Abstract

We show the equivalence of the convergence of Picard and Krasnoselskij, Mann, and Ishikawa iterations for the quasi-contraction mappings in convex metric spaces.

Published
2010

6. Comparison of the Rate of Convergence among Picard, Mann, Ishikawa, and Noor Iterations Applied to Quasicontractive Maps

Author

Billy E. Rhoades and Zhiqun Xue

Subjects
T57-57.97, QA299.6-433, Applied mathematics. Quantitative methods, Applied Mathematics, Mathematical analysis, Topology (electrical circuits), Differential geometry, Rate of convergence, Fixed-point iteration, Convergence (routing), Applied mathematics, Geometry and Topology, Analysis, Mathematics
Abstract

We provide sufficient conditions for Picard iteration to converge faster than Krasnoselskij, Mann, Ishikawa, or Noor iteration for quasicontractive operators. We also compare the rates of convergence between Krasnoselskij and Mann iterations for Zamfirescu operators.

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7. The convergence theorems of Ishikawa iterative process with errors for Φ-hemi-contractive mappings in uniformly smooth Banach spaces

Author

Zhiqun Xue, Billy E. Rhoades, and Guiwen Lv

Subjects
Discrete mathematics, Sequence, Iterative and incremental development, Differential geometry, Bounded function, Applied Mathematics, Regular polygon, Banach space, Geometry and Topology, Fixed point, Lipschitz continuity, Mathematics
Abstract

Let D be a nonempty closed convex subset of an arbitrary uniformly smooth real Banach space E, and be a generalized Lipschitz Φ-hemi-contractive mapping with . Let , , , be four real sequences in and satisfy the conditions (i) as and ; (ii) . For some , let , be any bounded sequences in D, and be an Ishikawa iterative sequence with errors defined by (1.1). Then (1.1) converges strongly to the fixed point q of T. A related result deals with the operator equations for a generalized Lipschitz and Φ-quasi-accretive mapping. MSC:47H10.

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