• Korea-Australia Rheology Journal
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• v.16 no.3
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• pp.117-128
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• 2004

The effect of molecular parameters on the steady vortex behaviors in the inertial viscoelastic flow past a cylinder has been investigated. FENE-CR model was considered as a constitutive equation. A recently developed iterative solution method (Kim et al., (in press)) was found to be successfully applicable to the computation of inertial viscoelastic flows. The high-resolution computations were carried out to understand the detailed flow behaviors based on the efficient iterative solution method armed with ILU(0) type pre-conditioner and BiCGSTAB method. The discrete elastic viscous split stress-G/streamline upwind Petrov Galerkin (DEVSS-G/SUPG) formulation was adopted as a stabilization method. The vortex size decreased as elasticity increases. However, the vortex enhancement was also observed in the case of large extensibility, which means that the vortex behavior is strongly dependent upon the material parameters. The longitudinal gradient of normal stress was found to retard the formation of vortex, whereas the extensional viscosity played a role in the vortex enhancement. The present results are expected to be helpful for understanding the inertial vortex dynamics of viscoelastic fluids in the flow past a confined cylinder.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.175-203
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• 2023

In this paper, we study an iterative algorithm that is based on inertial proximal and contraction methods embellished with relaxation technique, for finding common solution of monotone variational inclusion, and fixed point problems of pseudocontractive mapping in real Hilbert spaces. We establish a strong convergence result of the proposed iterative method based on prediction stepsize conditions, and under some standard assumptions on the algorithm parameters. Finally, some special cases of general problem are given as applications. Our results improve and generalized some well-known and related results in literature.

• Nonlinear Functional Analysis and Applications
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• v.26 no.4
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• pp.839-853
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• 2021

Let 𝕽ⁿ be an Euclidean space and g : 𝕽ⁿ → 𝕽ⁿ be a monotone and continuous mapping. Suppose the convex constrained nonlinear monotone equation problem x ∈ 𝕮 s.t g(x) = 0 has a solution. In this paper, we construct an inertial-type algorithm based on the three-term derivative-free projection method (TTMDY) for convex constrained monotone nonlinear equations. Under some standard assumptions, we establish its global convergence to a solution of the convex constrained nonlinear monotone equation. Furthermore, the proposed algorithm converges much faster than the existing non-inertial algorithm (TTMDY) for convex constrained monotone equations.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.131-164
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• 2024

In this research, we study a modified relaxed Tseng method with a single projection approach for solving common solution to a fixed point problem involving finite family of τ-demimetric operators and a quasi-monotone variational inequalities in real Hilbert spaces with alternating inertial extrapolation steps and adaptive non-monotonic step sizes. Under some appropriate conditions that are imposed on the parameters, the weak and linear convergence results of the proposed iterative scheme are established. Furthermore, we present some numerical examples and application of our proposed methods in comparison with other existing iterative methods. In order to show the practical applicability of our method to real word problems, we show that our algorithm has better restoration efficiency than many well known methods in image restoration problem. Our proposed iterative method generalizes and extends many existing methods in the literature.

• 한국기계연구소 소보
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• s.17
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• pp.99-109
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• 1987

Mechanisms with fully elastic members must consider both inertial forces due to the rigid motion of mechanisms and due to the elastic vibration of links. The main objectives of the kineto-elasto static and dynamic analyses are to calculate the quasi-static and the time-domain responses, respectively. An iterative transfer matrix method is used for a four-bar, fully elastic linked mechanism. Houbolt direct integration scheme is incorporated for the inertial effects due to the elastic link vibration. The analytical results are compared with the experimental responses and both responses show in good agreement.

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.203-221
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• 2022

In this paper, we introduce new hybrid inertial contraction projection algorithms for solving variational inequality problems over the intersection of the fixed point sets of demicontractive mappings in a real Hilbert space. The proposed algorithms are based on the hybrid steepest-descent method for variational inequality problems and the inertial techniques for finding fixed points of nonexpansive mappings. Strong convergence of the iterative algorithms is proved. Several fundamental experiments are provided to illustrate computational efficiency of the given algorithm and comparison with other known algorithms

• 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.

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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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.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.225-258
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• 2024

In this paper, we study the problem of finding a common solution to a fixed point problem involving a finite family of ρ-demimetric operators and a split monotone inclusion problem with monotone and Lipschitz continuous operator in real Hilbert spaces. Motivated by the inertial technique and the Tseng method, a new and efficient iterative method for solving the aforementioned problem is introduced and studied. Also, we establish a strong convergence result of the proposed method under standard and mild conditions.

• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.553-568
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• 2022

In this paper, we introduce and study two different iterative hybrid projection algorithms for solving a fixed point problem of nonexpansive mappings. The first algorithm is generated by the combination of the inertial method and the hybrid projection method. On the other hand, the second algorithm is constructed by the convex combination of three updated vectors and the hybrid projection method. The strong convergence of the two proposed algorithms are proved under very mild assumptions on the scalar control. For illustrating the advantages of these two newly invented algorithms, we created some numerical results to compare various numerical performances of our algorithms with the algorithm proposed by Dong and Lu [11].