• Nonlinear Functional Analysis and Applications
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• v.26 no.4
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• pp.717-731
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• 2021

In this paper, we introduce and study a new class of random generalized nonlinear implicit variational-like inclusion with random fuzzy mappings in a real separable Hilbert space and give its fixed point formulation. Using the fixed point formulation and the proximal mapping technique for strongly maximal monotone mapping, we suggest and analyze a random iterative scheme for finding the approximate solution of this class of inclusion. Further, we prove the existence of solution and discuss the convergence analysis of iterative scheme of this class of inclusion. Our results in this paper improve and generalize several known results in the literature.

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.1105-1114
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• 2021

In this paper, we prove a fixed point theorem for G-contractive type non-self mapping in cone metric space endowed with a graph. Our result generalizes many results in the literature and provide a new pavement for solving nonlinear functional equations.

• International Journal of CAD/CAM
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• v.8 no.1
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• pp.29-36
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• 2009

Domain mapping is a bijective transformation of one domain to another, usually from a complicated general domain to a chosen convex domain. This is directly useful in many application problems like shape modeling, morphing, texture mapping, shape matching, remeshing, path planning etc. A new approach considering the domain as made up of structural elements, like membranes or trusses, is developed and implemented using the nonlinear finite element formulation. The mapping is performed in two stages, boundary mapping and inside mapping. The boundary of the 3-D domain is mapped to the surface of a convex domain (in this case, a sphere) in the first stage and then the displacement/distortion of this boundary is used as boundary conditions for mapping the interior of the domain in the second stage. This is a general method and it develops a bijective mapping in all cases with judicious choice of material properties and finite element analysis. The consistent global parameterization produced by this method for an arbitrary genus zero closed surface is useful in shape modeling. Results are convincing to accept this finite element structural approach for domain mapping as a good method for many purposes.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.2
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• pp.458-466
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• 1998

In this work, a frequency domain method is tested numerically and experimentally to improve nonlinear model parameters using the frequency response function at the nonlinear element connected point of structure. This method extends the force-state mapping technique, which fits the nonlinear element forces with time domain response data, into frequency domain manipulations. The force-state mapping method in the time domain has limitations when applying to complex real structures because it needd a time domain lumped parameter model. On the other hand, the frequency domain method is relatively easily applicable to a complex real structure having nonlinear elements since it uses the frequency response function of each substurcture. Since this mehtod is performed in frequency domain, the number of equations required to identify the unknown parameters can be easily increased as many as it needed, just by not only varying excitation amplitude bot also selecting excitation frequency domain method has some advantages over the classical force-state mapping technique in the number of data points needed in curve fit and the sensitivity to response noise.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1453-1462
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• 2011

In this paper, we study a new class of generalized nonlinear variational-like inequalities in reflexive Banach spaces. By using the KKM technique and the concept of the Hausdorff metric, we obtain some existence results for generalized nonlinear variational-like inequalities with generalized monotone multi-valued mappings in Banach spaces. These results improve and generalize many known results in recent literature.

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.1021-1034
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• 2021

This paper deals with a nonlinear Langevin equation involving two fractional orders with three-point boundary conditions. Our aim is to find the existence of solutions for the proposed Langevin equation by using the Banach contraction mapping principle and the Krasnoselskii's fixed point theorem. Three examples are also given to show the significance of our results.

• Journal of Sensor Science and Technology
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• v.23 no.2
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• pp.99-104
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• 2014

Sensor arrays based on chemical sensors produce multidimensional patterns of data that may be used discriminate between different chemicals. For the human observer, visualization of multidimensional data is difficult, since the eye and brain process visual information in two or three dimensions. To devise a simple means of data inspection from the response of sensor arrays, PCA (Principal Component Analysis) or Sammon's nonlinear mapping technique can be applied. The PCA, which is a well-known statistical method and widely used in data analysis, has disadvantages including data distortion and the axes for plotting the dimensionally reduced data have no physical meaning in terms of how different one cluster is from another. In this paper, we have investigated two techniques and proposed a combination technique of PCA and nonlinear Sammom mapping for visualization of multidimensional patterns to two dimensions using data sets from odor sensing system. We conclude the combination technique has shown more advantages comparing with the PCA and Sammon nonlinear technique individually.

• Journal of the Korean Geotechnical Society
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• v.22 no.4
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• pp.5-10
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• 2006

A special finite difference method for nonlinear dynamic response analysis of semi-infinite foundation soil using mapping which transforms semi-infinite domain into finite domain is presented here. For the region of engineering interest, mapping is isometric, and fur far field, shrink mapping which transforms infinite interval into finite interval is adopted. At first, the responses of semi-infinite foundation soil with linear constituting model are computed, and compared with theoretical results and those of existing method. Good agreements are obtained among the results of the proposed method, Lamb's theory and FEM with extensive mesh model. Then the responses of infinite foundation soil are computed by the present method, using small and large mesh model. The results of small and large mesh models agree well with each other, demonstrating the effectiveness of the proposed method.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.933-951
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• 2015

In this paper, we consider the problem of convergence of an iterative algorithm for a general system of variational inequalities, a nonexpansive mapping and an ${\eta}$-strictly pseudo-contractive mapping. Strong convergence theorems are established in the framework of real Banach spaces.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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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.