• International Journal of Fuzzy Logic and Intelligent Systems
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• 제7권1호
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• pp.66-70
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• 2007

Note that Choquet integral is a generalized concept of Lebesgue integral, because two definitions of Choquet integral and Lebesgue integral are equal if a fuzzy measure is a classical measure. In this paper, we consider interval-valued Choquet integrals with respect to fuzzy measures(see [4,5,6,7]). Using these Choquet integrals, we define a mappings on the classes of Choquet integrable functions and give an example of a mapping defined by interval-valued Choquet integrals. And we will investigate some relations between m-convex mappings ${\phi}$ on the class of Choquet integrable functions and m-convex mappings $T_{\phi}$, defined by the class of closed set-valued Choquet integrals with respect to fuzzy measures.

• East Asian mathematical journal
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• 제26권5호
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• pp.703-714
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• 2010

A new class of nonlinear set-valued mixed variational inclusions involving (A, ${\eta}$)-accretive mappings in Banach spaces is introduced and studied, which includes many kind of variational inclusion (inequality) and complementarity problems as special cases. By using the resolvent operator associated with (A, ${\eta}$)-accretive operator due to Lan-Cho-Verma, the existence of solution for this kind of variational inclusion is proved, and a new hybrid proximal point algorithm is established and suggested, the convergence and stability theorems of iterative sequences generated by new iterative algorithms are also given in q-uniformly smooth Banach spaces.

• 호남수학학술지
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• 제27권2호
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• pp.251-265
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• 2005

In this paper, we introduce a generalized vector quasivariational like inequality for fuzzy mappings and show the existence of solutions under compact assumption.

• 호남수학학술지
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• 제27권3호
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• pp.445-463
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• 2005

In this paper, we introduce a Stampacchia type of generalized weak vector quasivariational-like inequalities for fuzzy mappings and consider the existence of solutions to them under non-compact assumption.

• 한국지능시스템학회:학술대회논문집
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• 한국지능시스템학회 2008년도 춘계학술대회 학술발표회 논문집
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• pp.127-128
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• 2008

In this paper, we consider define fuzzy invex sets and fuzzy preinvex functions on the class of Choquet integrable functions, and interval-valued fuzzy invex sets and interval-valued fuzzy preinvex functions on the class of interval-valued Choquet integrals. And also we prove some properties of them.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2000년도 추계학술대회 학술발표 논문집
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• pp.49-52
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• 2000

• East Asian mathematical journal
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• 제32권3호
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• pp.319-332
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• 2016

In this paper, we introduce the notion of generalized ${\alpha}-{\psi}$-Geraghty multivalued mappings and investigate the existence of a xed point of such multivalued mappings. We present a concrete example and an application on integral equations illustrating the obtained results.

• 대한수학회논문집
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• 제25권1호
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• pp.129-137
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• 2010

In this paper, we introduce and study a system of nonlinear set-valued implicit variational inclusions (SNSIVI) with relaxed cocoercive mappings in real Banach spaces. By using resolvent operator technique for M-accretive mapping, we construct a new class of iterative algorithms for solving this class of system of set-valued implicit variational inclusions. The convergence of iterative algorithms is proved in q-uniformly smooth Banach spaces. Our results generalize and improve the corresponding results of recent works.

• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.935-950
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• 2012

In this paper, we introduce and study a new system of generalized set-valued quasi-variational-like inclusions with (A, ${\eta}$)-accretive mapping in Banach spaces. By using the resolvent operator associated with (A, ${\eta}$)-accretive mappings, we construct a new iterative algorithm for approximating the solution of this system of variational inclusions. We also prove the existence of solutions and the convergence of the sequences generated by the algorithm in Banach spaces. The results presented in this paper extend and improve some known results in the literature.

• East Asian mathematical journal
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• 제25권1호
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• pp.45-53
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• 2009

In this paper, by using the technique of the resolvent operators, we study the behaviour and sensitivity analysis of the solutions set for a class of parametric completely generalized nonlinear variational inclusions with set-valued mappings.