• 충청수학회지
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• 제12권1호
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• pp.95-101
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• 1999

In this paper we prove a controlled convergence theorem for the Henstock integral by using new conditions.

• 자연과학논문집
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• 제17권1호
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• pp.51-54
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• 2006

확률변수의 랜덤 가중합에 대한 완전수렴 정리를 얻는다.

• 대한수학회논문집
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• 제24권2호
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• pp.227-237
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• 2009

In this paper, we introduce the Denjoy-Pettis integral of set-valued mappings and investigate some properties of the set-valued Denjoy-Pettis integral. Finally we obtain the Dominated Convergence Theorem and Monotone Convergence Theorem for set-valued Denjoy-Pettis integrable mappings.

• 충청수학회지
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• 제15권1호
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• pp.43-51
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• 2002

In this paper we prove a controlled convergence theorem for the Henstock integral by using the new conditions.

• 대한수학회지
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• 제55권4호
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• pp.833-848
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• 2018

In this paper we study the existence of conditional expectation for closed and convex valued Pettis-integrable random sets without assuming the Radon Nikodym property of the Banach space. New version of multivalued dominated convergence theorem of conditional expectation and multivalued $L{\acute{e}}vy^{\prime}s$ martingale convergence theorem for integrable and Pettis integrable random sets are proved.

• 대한수학회보
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• 제47권3호
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• pp.503-511
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• 2010

We prove a common fixed point theorem for S-contraction mappings without continuity. Using this result we obtain an approximating curve for S-nonexpansive mappings in a Banach space and prove Browder's type strong convergence theorem for this approximating curve. The demiclosedness principle for S-nonexpansive mappings is also established.

• 대한수학회보
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• 제44권3호
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• pp.493-506
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• 2007

In this paper weak and strong convergence theorems of modified Noor iterations to fixed points for asymptotically nonexpansive mappings in the intermediate sense in Banach spaces are established. In one theorem where we establish strong convergence we assume an additional property of the operator whereas in another theorem where we establish weak convergence assume an additional property of the space.

• 충청수학회지
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• 제21권3호
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• pp.327-337
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• 2008

In this paper, we prove strong convergence theorems of Halpern iteration for relatively asymptotically nonexpansive mappings in the framework of Banach spaces. Our results extend and improve the recent ones announced by [C. Martinez-Yanes, H. K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006), 2400-2411], [X. Qin, Y. Su, Strong convergence theorem for relatively nonexpansive mappings in a Banach space, Nonlinear Anal. 67 (2007), 1958-1965] and many others.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제10권4호
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• pp.269-274
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• 2010

After introducing many different types of prefilter convergence, we introduce an universal method to define various notions of compactness using cluster point and convergence of a prefilter and to prove the Tychonoff theorem using characterizations of ultra(maximal) prefilters.

• East Asian mathematical journal
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• 제24권1호
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• pp.27-33
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• 2008

The purpose of this paper is to establish the weak convergence theorem of Mann iterative sequence for nonexpansive mappings in probabilistic Hilbert spaces. In order to establish the weak convergence theorem, a new method was presented in this paper, that is method of mathematical expectation.