• 대한수학회논문집
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• 제28권2호
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• pp.243-267
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• 2013

This paper is dedicated to study a new class of general nonlinear random A-maximal $m$-relaxed ${\eta}$-accretive (so called (A, ${\eta}$)-accretive [49]) equations with random relaxed cocoercive mappings and random fuzzy mappings in $q$-uniformly smooth Banach spaces. By utilizing the resolvent operator technique for A-maximal $m$-relaxed ${\eta}$-accretive mappings due to Lan et al. and Chang's lemma [13], some new iterative algorithms with mixed errors for finding the approximate solutions of the aforesaid class of nonlinear random equations are constructed. The convergence analysis of the proposed iterative algorithms under some suitable conditions are also studied.

• East Asian mathematical journal
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• 제32권5호
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• pp.685-700
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• 2016

The main object of this work to introduced and studied a new class of fuzzy general nonlinear ordered random variational inequalities in ordered Banach spaces. By using the random B-restricted accretive mapping with measurable mappings ${\alpha},{\alpha}^{\prime}:{\Omega}{\rightarrow}(0,1)$, an existence of random solutions for this class of fuzzy general nonlinear ordered random variational inequality (equation) with fuzzy mappings is established, a random approximation algorithm is suggested for fuzzy mappings, and the relation between the first value $x_0(t)$ and the random solutions of fuzzy general nonlinear ordered random variational inequality is discussed.

• East Asian mathematical journal
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• 제34권1호
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• pp.47-58
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• 2018

In this paper, we consider a fuzzy nonlinear random variational inclusion problems involving ordered RME-multivalued mapping in ordered Banach spaces. By using the random relaxed resolvent operator and its properties, we suggest an random iterative algorithm. Finally both the existence of the random solution of the original problem and the convergence of the random iterative sequences generated by random algorithm are proved.

• East Asian mathematical journal
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• 제34권3호
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• pp.265-285
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• 2018

The main purpose of this paper, by using the resolvent operator technique associated with randomly (A, ${\eta}$, m)-accretive operator is to establish an existence and convergence theorem for a class of system of random nonlinear equations with fuzzy mappings in Banach spaces. Our works are improvements and generalizations of the corresponding well-known results.