• Nonlinear Functional Analysis and Applications
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• 제27권1호
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• pp.59-82
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• 2022

In this paper, we present a modified (improved) generalized M-iteration with the inertial technique for three quasi-nonexpansive multivalued mappings in a real Hilbert space. In addition, we obtain a weak convergence result under suitable conditions and the strong convergence result is achieved using the hybrid projection method with our modified generalized M-iteration. Finally, we apply our convergence results to certain optimization problem, and present some numerical experiments to show the efficiency and applicability of the proposed method in comparison with other improved iterative methods (modified SP-iterative scheme) in the literature. The results obtained in this paper extend, generalize and improve several results in this direction.

• Journal of applied mathematics & informatics
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• 제9권2호
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• pp.787-791
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• 2002

The aim of this paper is to study the condition of $\zeta$-convexity. We will give examples of $\zeta$-functions in filbert spaces and in non-UMD-spaces.

• Journal of applied mathematics & informatics
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• 제10권1_2호
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• pp.371-376
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• 2002

The aim of this paper is to study the condition of η-concavity. We will give examples of η-functions in Hilbert spaces on two different domains.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권2호
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• pp.137-149
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• 2006

We introduce the notion of the generalized covariance and variance for bounded linear operators on Hilbert space, and prove that the generalized covariance-variance inequality holds. It turns out that the inequality is a useful formula in tile study of inequality involving linear operators in Hilbert spaces.

• 대한수학회지
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• 제32권1호
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• pp.103-108
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• 1995

It is a well-known classical result of Mazur and Ulam that an isometry T from a real Banach space X onto a real Banach space Y with T(0) = 0 is automatically linear[5].

• 대한수학회논문집
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• 제13권2호
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• pp.273-280
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• 1998

We construct factors of type III and of type $II_\infty$ over the Hilbert spaces on the equivalence relations.

• 대한수학회논문집
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• 제14권1호
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• pp.157-169
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• 1999

We consider the C\ulcorner-algebra O\ulcorner generated by infinite isometries \ulcorner,\ulcorner, …on Hilbert spaces with the property \ulcorner \ulcorner$\leq$1 for every n$\in$N. We present certain type of representations of C\ulcorner-algerbra O\ulcorner on a separable Hilbert space and study the conditions for irreducibility of these representations.

• 대한수학회지
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• 제46권3호
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• pp.609-620
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• 2009

We establish some estimates on the hyper bilinear Hilbert transform on both Euclidean space and torus. We also use a transference method to obtain a Kenig-Stein's estimate on bilinear fractional integrals on the n-torus.

• 대한수학회논문집
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• 제10권2호
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• pp.401-407
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• 1995

The best constants for two distinct weak-type inequalities for martingales and their differential subordinates with values in some spaces isomorphic to a Hilbert space are shown to be the same. This extends the result of Burkholder shown in the Hilbert space setting.

• 대한수학회지
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• 제44권4호
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• pp.889-902
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• 2007

An existence theorem for a new class of parametric generalized mixed implicit quasi-variational inclusion problems is established in Hilbert spaces. Further, we study the behavior and sensitivity analysis of the solution set in this class of parametric variational inclusion problems.