http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
Jinlong Kang,Yongfu Su,Xin Zhang 한국전산응용수학회 2011 Journal of applied mathematics & informatics Vol.29 No.1
The purpose of this article is to prove strong convergence theorems for weak relatively nonexpansive mapping which is firstly presented in this article. In order to get the strong convergence theorems for weak relatively nonexpansive mapping, the monotone CQ iteration method is presented and is used to approximate the fixed point of weak relatively nonexpansive mapping, therefore this article apply above results to prove the strong convergence theorems of zero point for maximal monotone operators in Banach spaces. Noting that, the CQ iteration method can be used for relatively nonexpansive mapping but it cannot be used for weak relatively nonexpansive mapping. However, the monotone CQ method can be used for weak relatively nonexpansive mapping. The results of this paper modify and improve the results of S.Matsushita and W.Takahashi, and some others.
Kang, Jinlong,Su, Yongfu,Zhang, Xin The Korean Society for Computational and Applied M 2011 Journal of applied mathematics & informatics Vol.29 No.1
The purpose of this article is to prove strong convergence theorems for weak relatively nonexpansive mapping which is firstly presented in this article. In order to get the strong convergence theorems for weak relatively nonexpansive mapping, the monotone CQ iteration method is presented and is used to approximate the fixed point of weak relatively nonexpansive mapping, therefore this article apply above results to prove the strong convergence theorems of zero point for maximal monotone operators in Banach spaces. Noting that, the CQ iteration method can be used for relatively nonexpansive mapping but it can not be used for weak relatively nonexpansive mapping. However, the monotone CQ method can be used for weak relatively nonexpansive mapping. The results of this paper modify and improve the results of S.Matsushita and W.Takahashi, and some others.
A GENERAL ITERATIVE ALGORITHM FOR A FINITE FAMILY OF NONEXPANSIVE MAPPINGS IN A HILBERT SPACE
Sornsak Thianwan 한국전산응용수학회 2010 Journal of applied mathematics & informatics Vol.28 No.1
Let C be a nonempty closed convex subset of a real Hilbert space H. Consider the following iterative algorithm given by x0 2 C arbitrarily chosen,xn+1 = αnγf(Wnxn)+βnxn+((1−βn)I−αnA)WnPC(I−snB)xn, ∀n≥0,where γ > 0, B : C → H is a β-inverse-strongly monotone mapping, f is a contraction of H into itself with a coefficient α (0 < α < 1), Pc is a projection of H onto C, A is a strongly positive linear bounded operator on H and Wn is the W-mapping generated by a finite family of nonexpansive mappings T1, T2, ... TN and {λn,1}, {λn,2}, . . . , {λn,N}. Nonexpansivity of each Ti ensures the nonexpansivity of Wn. We prove that the sequence {χn} generated by the above iterative algorithm converges strongly to a common fixed point q ∈ F := ∩Ni=1F(Ti)∩VI(C,B) which solves the variational inequality <(γf − A)q, p − q>≤ 0 for all p ∈ F. Using this result, we consider the problem of finding a common fixed point of a finite family of nonexpansive mappings and a strictly pseudocontractive mapping and the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of zeros of an inverse-strongly monotone mapping. The results obtained in this paper extend and improve the several recent results in this area.
Strong Convergence of Modified Iteration Processes for Relatively Weak Nonexpansive Mappings
Boonchari, Daruni,Saejung, Satit Department of Mathematics 2012 Kyungpook mathematical journal Vol.52 No.4
We adapt the concept of shrinking projection method of Takahashi et al. [J. Math. Anal. Appl. 341(2008), 276-286] to the iteration scheme studied by Kim and Lee [Kyungpook Math. J. 48(2008), 685-703] for two relatively weak nonexpansive mappings. By letting one of the two mappings be the identity mapping, we also obtain strong convergence theorems for a single mapping with two types of computational errors. Finally, we improve Kim and Lee's convergence theorem in the sense that the same conclusion still holds without the uniform continuity of mappings as was the case in their result.
A NEW APPROXIMATION SCHEME FOR FIXED POINTSOF ASYMPTOTICALLY ø-HEMICONTRACTIVE MAPPINGS
Kim, Seung-Hyun,Lee, Byung-Soo Korean Mathematical Society 2012 대한수학회논문집 Vol.27 No.1
In this paper, we introduce an asymptotically $\phi$-hemicontractive mapping with a $\phi$-normalized duality mapping and obtain some strongly convergent result of a kind of multi-step iteration schemes for asymptotically $\phi$-hemicontractive mappings.
Birol Gunduz,Hemem Dutta 장전수학회 2017 Proceedings of the Jangjeon mathematical society Vol.20 No.3
In this paper, we first define nonself total asymptotically I-nonexpansive mappings and nonself total asymptotically I-quasi-nonexpansive mappings. Then, we prove weak and strong convergence theorems of a composite iterative process to a common fixed point of nonself total asymptotically quasi-nonexpansive map- pings and nonself total asymptotically I-quasi-nonexpansive mappings, defined on a nonempty closed convex subset of uniformly convex Banach space.
COMMON FIXED POINTS OF TWO NONEXPANSIVE MAPPINGS BY A MODIFIED FASTER ITERATION SCHEME
Safeer Hussain Khan,김종규 대한수학회 2010 대한수학회보 Vol.47 No.5
We introduce an iteration scheme for approximating common fixed points of two mappings. On one hand, it extends a scheme due to Agarwal et al. [2] to the case of two mappings while on the other hand,it is faster than both the Ishikawa type scheme and the one studied by Yao and Chen [18] for the purpose in some sense. Using this scheme,we prove some weak and strong convergence results for approximating common fixed points of two nonexpansive self mappings. We also outline the proofs of these results to the case of nonexpansive nonself mappings.
COMMON FIXED POINTS OF TWO NONEXPANSIVE MAPPINGS BY A MODIFIED FASTER ITERATION SCHEME
Khan, Safeer Hussain,Kim, Jong-Kyu Korean Mathematical Society 2010 대한수학회보 Vol.47 No.5
We introduce an iteration scheme for approximating common fixed points of two mappings. On one hand, it extends a scheme due to Agarwal et al. [2] to the case of two mappings while on the other hand, it is faster than both the Ishikawa type scheme and the one studied by Yao and Chen [18] for the purpose in some sense. Using this scheme, we prove some weak and strong convergence results for approximating common fixed points of two nonexpansive self mappings. We also outline the proofs of these results to the case of nonexpansive nonself mappings.
Common fixed points of mean nonexpansive mappings in Cat(0) spaces
S. H. Khan,S. Ritika 장전수학회 2020 Proceedings of the Jangjeon mathematical society Vol.23 No.4
In this paper, we consider a recently introduced three step iterative process but extended to the case of two mappings in CAT(0) spaces. We give new examples of two mappings which are mean nonex- pansive but not nonexpansive and possess a common fixed point. We establish ∆-convergence and weak convergence results for this iterative process for approximating common fixed points of two mean nonexpan- sive mappings. The results obtained in this paper extend and improve the recent ones announced by many authors in the sense that both our class of mappings and the iterative process are more general. Moreover, our results remain true for the spaces contained in CAT(0) spaces like Banach spaces and R-trees etc.
Safeer Hussain Khan,Ritika,Vishnu Narayan Mishra 한국전산응용수학회 2021 Journal of Applied and Pure Mathematics Vol.3 No.1
CAT(0) spaces contain a number of spaces including both linear and nonlinear ones. The class of generalized asymptotically quasi-nonexpansive mappings is a very wide class of mappings. Iterative processes are used to approximate solutions when actual one is hard to find. In this paper, we prove strong convergence results using a three step iterative process for generalized asymptotically quasi-nonexpansive mappings in CAT(0) spaces. Our results remain valid in both linear and nonlinear domains. Thus our results generalize the corresponding results of many authors.