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강신민,Yuguang Xu,Zeqing Liu 영남수학회 2008 East Asian mathematical journal Vol.24 No.3
The purpose of this paper is to study the existence and uniqueness of the fixed point of uniformly pseudo-contractive operator and the solution of equation with uniformly accretive operator, and to approximate the xed point and the solution by the Mann iterative sequence in an arbitrary Banach space or an uniformly smooth Banach space respectively. The results presented in this paper show that if X is a real Banach space and A : X -> X is an uniformly accretive operator and (I-A)X is bounded then A is a mapping onto X when A is continuous or X* is uniformly convex and A is demicontinuous. Consequently, the corresponding results which depend on the assumptions that the fixed point of operator and solution of the equation are in existence are improved.
Xu, Yuguang,Liu, Zeqing,Kang, Shin-Min The Youngnam Mathematical Society Korea 2008 East Asian mathematical journal Vol.24 No.3
The purpose of this paper is to study the existence and uniqueness of the fixed point of uniformly pseudo-contractive operator and the solution of equation with uniformly accretive operator, and to approximate the fixed point and the solution by the Mann iterative sequence in an arbitrary Banach space or an uniformly smooth Banach space respectively. The results presented in this paper show that if X is a real Banach space and A : X $\rightarrow$ X is an uniformly accretive operator and (I-A)X is bounded then A is a mapping onto X when A is continuous or $X^*$ is uniformly convex and A is demicontinuous. Consequently, the corresponding results which depend on the assumptions that the fixed point of operator and solution of the equation are in existence are improved.
Lan, Heng-You 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.25 No.1
In this work, by using Xu's inequality, Nalder's results, the notion of $(A,\;{\eta})-accretive$ mappings and the new resolvent operator technique associated with $(A,\;{\eta})-accretive$ mappings due to Lan et al., we study the existence of solutions for a new class of $(A,\;{\eta})-accretive$ variational inclusion problems with non-accretive set-valued mappings and the convergence of the iterative sequences generated by the algorithms in Banach spaces. Our results are new and extend, improve and unify the corresponding results in this field.
SYSTEM OF GENERALIZED MULTI-VALUED RESOLVENT EQUATIONS: ALGORITHMIC AND ANALYTICAL APPROACH
Javad Balooee,Shih-sen Chang,Jinfang Tang Korean Mathematical Society 2023 대한수학회보 Vol.60 No.3
In this paper, under some new appropriate conditions imposed on the parameter and mappings involved in the resolvent operator associated with a P-accretive mapping, its Lipschitz continuity is proved and an estimate of its Lipschitz constant is computed. This paper is also concerned with the construction of a new iterative algorithm using the resolvent operator technique and Nadler's technique for solving a new system of generalized multi-valued resolvent equations in a Banach space setting. The convergence analysis of the sequences generated by our proposed iterative algorithm under some appropriate conditions is studied. The final section deals with the investigation and analysis of the notion of H(·, ·)-co-accretive mapping which has been recently introduced and studied in the literature. We verify that under the conditions considered in the literature, every H(·, ·)-co-accretive mapping is actually P-accretive and is not a new one. In the meanwhile, some important comments on H(·, ·)-co-accretive mappings and the results related to them appeared in the literature are pointed out.
Kim, Jong Kyu,Truong, Minh Tuyen Korean Mathematical Society 2017 대한수학회지 Vol.54 No.6
In this paper we introduce a new iterative method by the combination of the prox-Tikhonov regularization and the alternating resolvents for finding a common zero of two accretive operators in Banach spaces. And we will give some applications and numerical examples. The results of this paper improve and extend the corresponding results announced by many others.
NEW ITERATIVE ALGORITHMS FOR ZEROS OF ACCRETIVE OPERATORS
Song, Yisheng Korean Mathematical Society 2009 대한수학회지 Vol.46 No.1
Two new iterative algorithms are provided to find zeros of accretive operators in a Banach space E with a uniformly $G\hat{a}teaux$ differentiable norm. Strong convergence for two iterations is proved and as applications, the viscosity approximation results are obtained also.
Strong Convergence Theorems for Common Points of a Finite Family of Accretive Operators
Jeong, Jae Ug,Kim, Soo Hwan Department of Mathematics 2019 Kyungpook mathematical journal Vol.59 No.3
In this paper, we propose a new iterative algorithm generated by a finite family of accretive operators in a q-uniformly smooth Banach space. We prove the strong convergence of the proposed iterative algorithm. The results presented in this paper are interesting extensions and improvements of known results of Qin et al. [Fixed Point Theory Appl. 2014(2014): 166], Kim and Xu [Nonlinear Anal. 61(2005), 51-60] and Benavides et al. [Math. Nachr. 248(2003), 62-71].
New iterative algorithms for zeros of accretive operators
Yisheng Song 대한수학회 2009 대한수학회지 Vol.46 No.1
Two new iterative algorithms are provided to find zeros of accretive operators in a Banach space E with a uniformly Gateaux differentiable norm. Strong convergence for two iterations is proved and as applications, the viscosity approximation results are obtained also. Two new iterative algorithms are provided to find zeros of accretive operators in a Banach space E with a uniformly Gateaux differentiable norm. Strong convergence for two iterations is proved and as applications, the viscosity approximation results are obtained also.
Approximation common zero of two accretive operators in banach spaces
Kim, J.K.,Tuyen, T.M. Elsevier [etc.] 2016 Applied mathematics and computation Vol.283 No.-
<P>The purpose of this paper is to introduce a new iterative method that is the combination of the proximal point algorithm, viscosity approximation method and alternating resolvent method for finding the common zeros of two accretive operators in Banach spaces. And we will prove the strong convergence theorems for the iterative algorithms and give the example of the main theorems. The results of this paper are improvements and extensions of the corresponding ones announced by many others. (c) 2016 Elsevier Inc. All rights reserved.</P>
ITERATIVE SOLUTION OF NONLINEAR EQUATIONS WITH STRONGLY ACCRETIVE OPERATORS IN BANACH SPACES
Jeong, Jae-Ug 한국전산응용수학회 2000 Journal of applied mathematics & informatics Vol.7 No.2
Let E be a real Banach space with property (U,${\lambda}$,m+1,m);${\lambda}{\ge}$0; m${\in}N$, and let C be a nonempty closed convex and bounded subset of E. Suppose T: $C{\leftrightarro}C$ is a strongly accretive map, It is proved that each of the two well known fixed point iteration methods( the Mann and Ishikawa iteration methods.), under suitable conditions , converges strongly to a solution of the equation Tx=f