• 대한수학회논문집
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• 제26권4호
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• pp.575-584
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• 2011

We provide a semilocal convergence analysis for a Newtonlike method under weak conditions in a Banach space setting. In particular, we only assume that the Gateaux derivative of the operator involved is hemicontinuous. An application is also provided.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.325-336
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• 2008

In this paper, we prove the weak and strong convergence of the three-step iterative scheme with errors to a common fixed point for two asymptotically nonexpansive mappings in a uniformly convex Banach space under a condition weaker than compactness. Our theorems improve and generalize some previous results.

• 대한수학회논문집
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• 제35권3호
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• pp.907-916
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• 2020

In this paper, we introduce the notion of p-distance in a complex uncertain sequence space. By using the concepts of p-distance, we give some theorems of convergence. Also, in a complex uncertain sequence space, we develope some properties on convergence in measure.

• 대한수학회논문집
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• 제28권1호
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• pp.135-141
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• 2013

In this paper, we first talk about a more wide class of nonlinear mappings, Then, we deal with weak convergence theorems for generalized hybrid mappings in a Hilbert space.

• 한국지능시스템학회논문지
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• 제17권1호
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• pp.143-147
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• 2007

With a new ordinary norm as an analogy of Krishna and Sarma[5] and Bag and Samanta[1], we will characterize the notions of the convergence of the sequences of fuzzy points, the fuzzy, ${\alpha}$-Cauchy sequence and fuzzy completeness.

• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.93-100
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• 2012

In this paper, we present a strongly convergent parallel projection algorithm by introducing some parameter sequences for convex feasibility problem. To prove the strong convergence in a simple way, we transmit the parallel algorithm in the original space to an alternating one in a newly constructed product space. Thus, the strong convergence of the parallel projection algorithm is derived with the help of the alternating one under some parametric controlling conditions.

• 대한수학회지
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• 제57권3호
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• pp.553-570
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• 2020

In this paper, we establish complete convergence for sequences of extended independent random variables and arrays of rowwise extended independent random variables under sub-linear expectations in Peng's framework. The results obtained in this paper extend the corresponding ones of Baum and Katz [1] and Hu and Taylor [11] from classical probability space to sub-linear expectation space.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권1호
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• pp.13-18
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• 2009

A semilocal convergence analysis is provided for Newton's method in a Banach space. The inverses of the operators involved are only locally $H{\ddot{o}}lderian$. We make use of a point-based approximation and center-$H{\ddot{o}}lderian$ hypotheses for the inverses of the operators involved. Such an approach can be used to approximate solutions of equations involving nonsmooth operators.

• East Asian mathematical journal
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• 제24권3호
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• pp.295-304
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• 2008

We approximate a locally unique solution of a nonlinear operator equation containing a non-differentiable operator in a Banach space setting using Newton's method. Sufficient conditions for the semilocal convergence of Newton's method in this case have been given by several authors using mainly increasing sequences [1]-[6]. Here, we use center as well as Lipschitz conditions and decreasing majorizing sequences to obtain new sufficient convergence conditions weaker than before in many interesting cases. Numerical examples where our results apply to solve equations but earlier ones cannot [2], [5], [6] are also provided in this study.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.525-536
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• 2007

In this paper, we prove the weak and strong convergence of the Noor iterative scheme to a common fixed point for two asymptotically nonexpansive mappings in a uniformly convex Banach space under a condition weaker than compactness. Our theorems improve and generalize some previous results.