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9 results on '"ZHIQUN XUE"'

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

Author

Zhiqun Xue

Subjects
*SPEED, *STOCHASTIC convergence, *ITERATIVE methods (Mathematics), *BANACH spaces, *FIXED point theory
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). [ABSTRACT FROM AUTHOR]

Published
2008
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3. Iterative approximation with errors of fixed point for a class of nonlinear operator with a bounder range.

Author

Zhiqun, Xue and Haiyun, Zhou

Subjects
*COUPLINGS (Gearing), *BANACH spaces, *STRUCTURAL plates, *NONLINEAR operators, *STRUCTURAL stability, *ITERATIVE methods (Mathematics)
Abstract

Let X be a uniformly smooth real Banach space. Let T:X → X be continuos and strongly accretive operator. For a given f ε X, define S: X → X by Sx =f−Tx+x, for all x ε X. Let {an}, {βn}be two real sequences in (0, 1) satisfying:; Assume that {un} and {υn} are two sequences in X satisfying |un| = 0(αn) and |υn| → 0 as n → ∞. For arbitrary x0 ε X, the iteration sequence {xn} is defined by Moreover, suppose that {Sxn} and {Syn} are bounded, then {xn} converges strongly to the unique fixed point of S. [ABSTRACT FROM AUTHOR]

Published
1999
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4. A further remark to paper ‘Convergence theorems for the common solution for a finite family of ϕ-strongly accretive operator equations’

Author

Zhiqun Xue and Haiyun Zhou

Subjects
Discrete mathematics, Uniform continuity, Operator (computer programming), Applied Mathematics, Convergence (routing), Banach space, Discrete Mathematics and Combinatorics, Analysis, Mathematics
Abstract

In this note, we point out several gaps in Gurudwan and Sharma (Appl. Math. Comput. 217(15):6748-6754, 2011) and Yang (Appl. Math. Comput. 218(21):10367-10369, 2012) and give the main results under weaker conditions. MSC: 47H10; 47H09; 46B20

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5. 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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6. The convergence of the modified Mann and Ishikawa iterations in Banach spaces

Author

Guiwen Lv and Zhiqun Xue

Subjects
Pure mathematics, Applied Mathematics, Mathematical analysis, Convergence (routing), Banach space, Discrete Mathematics and Combinatorics, Uniformly convex space, Fixed point, Analysis, Mathematics
Abstract

In this paper, under the new condition we show that the convergence of the modified Mann and Ishikawa iterations is equivalent for uniformly L-Lipschitz asymptotically pseudocontractive mappings in real Banach spaces. Our results extend and improve the corresponding results of Zeng (Acta Math. Sin. 47:219-228, 2004).

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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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8. The convergence of implicit Mann and Ishikawa iterations for weak generalized φ-hemicontractive mappings in real Banach spaces

Author

Fang Zhang and Zhiqun Xue

Subjects
Discrete mathematics, Nonlinear system, Applied Mathematics, Convergence (routing), Regular polygon, Banach space, Existence theorem, Discrete Mathematics and Combinatorics, Fixed point, Analysis, Mathematics
Abstract

Let E be a real Banach space and let D be a nonempty closed convex subset of E ,l et T : D → D be a continuous weak generalized ϕ-hemicontractive mapping. The existence theorem of a fixed point of a weak generalized ϕ-pseudocontractive mapping is obtained. And we also prove that implicit Mann and Ishikawa iterations converge strongly to the unique fixed point of T. Our results extend the corresponding results of Xiang (Nonlinear Anal. 70(6): 2277-2279, 2009). MSC: Primary 47H09; 47J25

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9. Implicit iteration scheme for two phi-hemicontractive operators in arbitrary Banach spaces

Author

Zhiqun Xue, Guiwen Lv, and Arif Rafiq

Subjects
Discrete mathematics, Approximation property, Scheme (mathematics), Applied Mathematics, Convergence (routing), Banach space, Common fixed point, Regular polygon, Discrete Mathematics and Combinatorics, Banach manifold, Analysis, Mathematics
Abstract

The purpose of this paper is to characterize conditions for the convergence of the implicit Ishikawa iterative scheme with errors in the sense of Agarwal et al. (J. Math. Anal. Appl. 272:435-447, 2002) to a common fixed point of two ϕ-hemicontractive mappings in a nonempty convex subset of an arbitrary Banach space.

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