ISHIKAWA TYPE ITERATIVE SEQUENCES WITH ERRORS FOR LIPSCHITZIAN φ-STRONGLY ACCRETIVE OPERATOR EQUATIONS IN ARBITRARY BANACH SPACES

In this paper, we investigate the problem of approximating solutions of the equations of Lipschitzian ψ-strongly accretive operators and fixed points of Lipschitzian ψ-hemicontractive operators by lshikawa type iterative sequences with errors. Our results unify, improve and extend the results obtained previously by several authors including Li and Liu (Acta Math. Sinica 41 (4)(1998), 845-850), and Osilike (Nonlinear Anal. TMA, 36(1)(1999), 1-9), and also answer completely the open problems mentioned by Chidume (J. Math. Anal. Appl. 151 (2)(1990), 453-461).

AN ITERATIVE PROCESS FOR FINDING APPROXIMATE SOLUTIONS TO NONLINEAR EQUATIONS OF STRONGLY ACCRETIVE OPERATORS

In this paper, we investigate the Ishikawa iteration process in a p-uniformly smooth Banach space X. We prove that the Ishikawa iteration process converges strongly to the unique solution of the equation Tx=f when T is a Lipschitzian and strongly accretive operator frow X to X, or to the unique fixed point of T when T is a Lipschitzian and strictly pseudocontractive mapping from a nonempty closed convex subset K of X into itself. Our results are the extension and improvements of the earlier and recent results in this field.

REGULARIZATION METHODS FOR NONLINEAR ILL-POSED PROBLEMS WITH ACCRETIVE OPERATORS

This article is devoted to the regularization of nonlinear ill-posed problems with accretive operators in Banach spaces. The data involved are assumed to be known approximately. The authors concentrate their discussion on the convergence rates of regular solutions.

A New System of Variational Inclusions with （H,η）-accretive Operators in Banach Spaces

在这份报纸，我们首先介绍说出的概括 accretive 操作员的一个新班( H ，)在学习性质的 Banach space.By 的 -accretive ( H ，) -accretive,we 扩大与 m-accretive 操作员联系到的溶剂操作员的概念新( H ，)新溶剂操作员技术的 -accretive operators.In 术语，我们证明变化 inclusions.We 的这个新系统的解决方案的存在和唯一也为接近构造一个新算法这个系统和 dis

ITERATIVE PROCESS TO -HEMICONTRACTIVE OPERATOR AND-STRONGLY ACCRETIVE OPERATOR EQUATIONS

Let E be an arbitrary real Banach space and K be a nonempty closed convex subsets of E. Let T:K→K be a uniformly continuous _hemicontractive operator with bounded range and a n,b n,c n,a ′ n,b ′ n,c ′ n be sequences in [0,1] satisfying:ⅰ) a n+b n+c n=a ′ n+b ′ n+c ′ n=1. n≥0; ⅱ) lim b n= lim b ′ n= lim c ′ n= 0; ⅲ)∑∞n=0b n=∞; ⅳ) c n=o(b n). For any given x 0,u 0,v 0∈K, define the Ishikawa type iterative sequence x n as follows: x n+1 =a nx n+b nTy n+c nu n, y n=a ′ nx n+b ′ nTx n+c ′ nv n (n≥0), where u n and v n are bounded sequences in K. Then x n converges strongly to the unique fixed point of T. Related result deals with the convergence of Ishikawa type iterative sequence to the solution of _strongly accretive operator equations.

<i>H</i>(.,.)<i>- φ - η -</i>Accretive Operators and Generalized Variational-Like Inclusions

In this paper, we generalize H(.,.) accretive operator introduced by Zou and Huang [1] and we call it H(.,.)- φ - η - accretive operator. We define the resolvent operator associated with H(.,.)- φ - η - accretive operator and prove its Lipschitz continuity. By using these concepts an iterative algorithm is suggested to solve a generalized variational-like inclusion problem. Some examples are given to justify the definition of H(.,.)- φ - η - accretive operator.

Generalized H-η-accretive operators in Banach spaces with application to variational inclusions

In this paper, a new notion of a generalized H-η-accretive operator is introduced and studied, which provides a unifying framework for the generalized m-accretive operator and the H-η-monotone operator in Banach spaces. A resolvent operator associated with the generalized H-η-accretive operator is defined, and its Lipschitz continuity is shown. As an application, the solvability for a class of variational inclusions involving the generalized H-η-accretive operators in Banach spaces is considered. By using the technique of the resolvent mapping, an iterative algorithm for solving the variational inclusion in Banach spaces is constructed. Under some suitable conditions, it is proven that the solution for the variational inclusion and the convergence of the iterative sequence generated by the algorithm exist.

A Note on Iterative Solutions of Nonlinear Accretive Operator Equations

Suppose that X is a real Banach space, H: X→X is a Lipschitz operator, T: X→X is a uniformly continuous operator with bounded range, and H+T is strongly accretive. Then the Ishikawa iteration process converges strongly to the unique solution of the equation Hx+Tx=f . This conclusion extends the corresponding results in recent papers.

ITERATIVE REGULARIZATION METHODS FOR NONLINEAR ILL-POSED OPERATOR EQUATIONS WITH M-ACCRETIVE MAPPINGS IN BANACH SPACES

In this paper, a modified Newton type iterative method is considered for ap- proximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is obtained based on an a priori choice of the regularization parameter. Our analysis is not based on the sequential continuity of the normalized duality mapping.

Convergence Theorems of Mann and Ishikawa Iterative Processes with Errors for Multivalued Φ-strongly Accretive Mapping

Let X be a real Banach space and A : X→ 2x a bounded uniformly continuous Φ-strongly accretive multivalued mapping. For any f ∈ X, Mann and Ishikawa iterative processes with errors converge strongly to the unique solution of Ax (?) f. The conclusion in this paper weakens the stronger conditions about errors in Chidume and Moore's theorem (J. Math. Anal. Appl, 245(2000), 142-160).

ISHIKAWA ITERATIVE PROCESS FOR CONSTRUCTING SOLUTIONS OF m-ACCRETIVE OPERATOR EQUATIONS

The convergence of the Ishikawa iteration sequences with errors for constructing solutions of m-accretive operator equations is characterized. Moreover, the error estimates of approximate solutions for locally Lipschitzian and m-accretive operator equations are established.

Approximation Solutions of Nonlinear Strongly Accretive Operator Equations by Ishikawa Iteration Procedure with Errors

<正>Let 1＜ρ≤2,E be a real ρ-uniformly smooth Banach space and T:E→E be a continuous and strongly accretive operator.The purpose of this paper is to investigate the problem of approximating solutions to the equation Tx=f by the Ishikawa iteration procedure with errors (?) where x_0 ∈ E,{u_n},{υ_n}are bounded sequences in E and{α_n},{b_n},{c_n},{a_n~'},{b_n~'},{c_n~'} are real sequences in[0,1].Under the assumption of the condition 0＜α≤b_n+c_n,An≥0, it is shown that the iterative sequence{x_n}converges strongly to the unique solution of the equation Tx=f.Furthermore,under no assumption of the condition(?)(b_n~'+c_n~')=0,it is also shown that{x_n}converges strongly to the unique solution of Tx=f.

Approximative Method of Fixed Point for Φ-Pseudocontractive Operator and an Application to Equation with Accretive Operator

In this paper, Φ-pseudo-contractive operators and Φ-accretive operators, more general than the strongly pseudo-contractive operators and strongly accretive operators, are introduced. By setting up a new inequality, authors proved that if ?is a uniformly continuous Φ-pseudo-contractive operator then T has unique fixed point q and the Mann iterative sequence with random errors approximates to q. As an application, the iterative solution of nonlinear equation with Φ-accretive operator is obtained. The results presented in this paper improve and generalize some corresponding results in recent literature.

昆钢2号高炉炉况失常的原因及处理措施

对昆钢2号高炉2023年4月8日发生的炉况失常的原因及处理措施进行分析总结。认为这次炉况失常的直接原因是风口小套长时间漏水和炉墙黏结,间接原因是高炉计划检修周期过长、烧结矿冶金性能劣化、熔剂质量波动造成渣相波动和炉顶洒水效果不好。从装料制度、送风制度、造渣制度、热制度等方面进行系统调整,主要通过采取缩矿批退负荷、集中加焦、调整布料矩阵、增加水量提高冷却强度等措施,炉况实现快速恢复。4月12日,2号高炉焦炭负荷提升至4.54,日产量恢复到7058.789t/d,燃料比稳定在516kg/t。

湘钢2号高炉炉身上部结瘤的原因及处理

对湘钢2号高炉炉身上部结瘤的原因及处理进行了阐述。2号高炉从炉墙轻微结厚,逐步发展成为较为严重的结瘤,瘤体厚度达800mm以上,分析结瘤的原因,主要是块矿入炉粉末多及烧结矿质量劣化,炉内碱金属循环富集现象严重,炉身中上部冷却强度过大。根据2号高炉自身实际状况,采用物理击打法消除结瘤,实现了炉况的快速恢复,生产指标明显改善。这次结瘤处理过程教训深刻,认为高炉操作炉型的维护应以预防为主,无论是结厚还是结瘤,预防是关键,处理要及早,不能犹豫不决。

Strong Convergence Theorems of Viscosity Approximation for Accretive Operators

Let E be a real Banach space and let A be an m-accretive operator with a zero. Define a sequence {x_n} as follows:x_n+1=α_nf(x_n)+(1-α_n)J_r_n x_n,where {α_n},{r_n} are sequences satisfying certain conditions,and J_r denotes the resolvent(I+rA)^(-1)for r>1.Strong convergence of the algorithm {x_n} is obtained provided that E either has a weakly continuous duality map or is uniformly smooth.

ITERATIVE APPROXIMATION WITH ERRORS OF FIXED POINT FOR A CLASS OF NONLINEAR OPERATOR WITH A BOUNDED RANGE

Let X be a uniformly smooth real Banach space. tri T:X→X be a con-tinuous and strongly accretive operator. For a given f∈X,define S: X→X by 1)satisfying: Moreover, suppose that {Sxn} and {Syn} are bounded, then {Xn} converges strongly to the unique fixed point of S.

Viscosity Approximations by Generalized Contractions for Resolvents of Accretive Operators in Banach Spaces

In this paper, we prove a strong convergence theorem for resolvents of accretive operators in a Banach space by the viscosity approximation method with a generalized contraction mapping. The proximal point algorithm in a Banach space is also considered. The results extend some very recent theorems of W. Takahashi.

A Note on Modified Mann Accretive Iterations for Zero Points of Operators

A more general form of modified Mann iterations which converges strongly to a zero point of an m-accretive operator is given.The work in this paper is an extension and complement of the corresponding result of Kim T.H.and Xu H.K in

关于Chidume-Zegeye-Ntatin定理的注释

带误差的Mann迭代及Ishikawa迭代一直众多学者关心的一个热点问题。本文中我们对Chidume-Zegeye-Ntatin定理进行探讨,具体工作如下:首先是定理中序列有界性的证明进行了改进;其次用更为简单的方法证明了该定理;最后所得结果推广和改进了相关的结论。