• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.517-526
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• 2024

In this paper, some iterative methods are used to discuss the behavior of general mixed-harmonic variational inequalities. We employ the auxiliary principle technique and g-strongly harmonic monotonicity of the operator to obtain results on the existence of solutions to a generalized class of mixed harmonic variational inequality.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.545-558
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• 2024

In this study, a class of nonlinear boundary fractional Caputo Volterra-Fredholm integro-differential equations (CV-FIDEs) is taken into account. Under specific assumptions about the available data, we firstly demonstrate the existence and uniqueness features of the solution. The Gronwall's inequality, a adequate singular Hölder's inequality, and the fixed point theorem using an a priori estimate procedure. Finally, a case study is provided to highlight the findings.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.707-721
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• 2013

In this paper, we investigate a fuzzy version of stability theory for the following functional equation f(x+y)+f(x-y)-2f(x)-f(y)-f(-y)=0 in the sense of M. Mirmostafaee and M. S. Moslehian.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.507-517
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• 2009

We prove a functional central limit theorem for a linear random field generated by negatively associated multi-dimensional random variables. Under finite second moment condition we extend the result in Kim, Ko and Choi[Kim,T.S, Ko,M.H and Choi, Y.K.,2008. The invariance principle for linear multi-parameter stochastic processes generated by associated fields. Statist. Probab. Lett. 78, 3298-3303] to the negatively associated case.

• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.843-854
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• 2012

In this paper, the iterative Uzawa method with a modified Lagrangian functional is investigated to seek a saddle point for the semicoercive variational Signorini inequality.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.153-162
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• 1995

Ky Fan's minimax inequality is an important tool in nonlinear functional analysis and its applications, e.g. game theory and economic theory. Since Fan gave his minimax inequality in [2], various extensions of this interesting result have been obtained (see [4,11] and the references therein). Using Fan's minimax inequality, Ha [6] obtained a non-compact version of Sion's minimax theorem in topological vector spaces, and next Geraghty-Lin [3], Granas-Liu [4], Shih-Tan [11], Simons [12], Lin-Quan [10], Park-Bae-Kang [17], Bae-Kim-Tan [1] further generalize Fan's minimax theorem in more general settings. In [9], using the concept of submaximum, Komiya proved a topological minimax theorem which also generalized Sion's minimax theorem and another minimax theorem of Ha in [5] without using linear structures. And next Lin-Quan [10] further generalizes his result to two function versions and non-compact topological settings.

• International Journal of Control, Automation, and Systems
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• v.6 no.4
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• pp.515-525
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• 2008

In this paper, the problem of delay-dependent stabilization for singular systems with multiple internal and external incommensurate constant point delays is investigated. The condition when a singular system subject to point delays is regular independent of time delays is given and it can be easily test with numerical or algebraic methods. Based on Lyapunov-Krasovskii functional approach and the descriptor integral-inequality lemma, a sufficient condition for delay-dependent stability is obtained. The main idea is to design multiple memoryless state feedback control laws such that the resulting closed-loop system is regular independent of time delays, impulse free, and asymptotically stable via solving a strict linear matrix inequality (LMI) problem. An explicit expression for the desired memoryless state feedback control laws is also given. Finally, a numerical example illustrates the effectiveness and the availability for the proposed method.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.373-380
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• 2021

If $p(z)={\sum\limits_{{\nu}=0}^{n}}a_{\nu}z^{\nu}$ is a polynomial of degree n having all its zeros on |z| = k, k ≤ 1, then Govil [3] proved that $${\max\limits_{{\mid}z{\mid}=1}}\;{\mid}p^{\prime}(z){\mid}\;{\leq}\;{\frac{n}{k^n+k^{n-1}}}\;{\max\limits_{{\mid}z{\mid}=1}}\;{\mid}p(z){\mid}$$. In this paper, by involving certain coefficients of p(z), we not only improve the above inequality but also improve a result proved by Dewan and Mir [2].

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.149-167
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• 2022

In this paper, we propose a viscosity iterative algorithm for approximating a common solution of finite family of variational inequality problem and fixed point problem for finite family of multi-valued type-one demicontractive mappings in real Hilbert spaces. A strong convergence result of the aforementioned problems were proved and some consequences of our result was also displayed. In addition, we discuss an application of our main result to convex minimization problem. The result presented in this article complements and extends many recent results in literature.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.205-235
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• 2023

In this paper, we introduce and study an iterative technique for solving quasimonotone split variational inequality problems and fixed point problem in the framework of real Hilbert spaces. Our proposed iterative technique is self adaptive, and easy to implement. We establish that the proposed iterative technique converges strongly to a minimum-norm solution of the problem and give some numerical illustrations in comparison with other methods in the literature to support our strong convergence result.