• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.587-601
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• 2022

In this article, we introduce the concept of contractive mapping, which is generally weak in metric spaces, and show the existence and uniqueness of the fixed point for such mapping in a metric space.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.261-269
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• 2022

The purpose of this paper is to introduce a new generalization class of cyclic mappings, called cyclic generalized 𝜑-weak contraction and obtain a corresponding best proximity point theorem for this cyclic mapping under certain conditions.

• Kyungpook Mathematical Journal
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• v.47 no.1
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• pp.77-79
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• 2007

In this note we point out how a theorem of Gamelin and Garnett from function theory can be used to establish a spectral mapping theorem for an arbitrary contraction and an associated class of $H^{\infty}$-functions.

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.601-610
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• 2021

A convergence theorem for a generalized 𝜑-weakly contractive mapping is proved which satisfy a generalized contraction condition on a complete metrically convex metric space. The result in this paper generalizes the relevant results due to Rhoades [18], Alber and Guerre-Delabriere [1], Khan and Imdad [14], Xue [20] and others. An illustrative example is also furnished in support of our main result.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.731-742
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• 2022

In this paper, we present a new mixed type iterative process for approximating the common fixed points of single-valued nonexpansive mapping and multi-valued nonexpansive mapping in a CAT(0) space. We demonstrate strong and weak convergence theorems for the new iterative process in CAT(0) spaces, as well as numerical results to support our theorem.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.509-524
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• 2023

In this study, we characterize the structure of the multivariable mappings which are sextic in each component. Indeed, we unify the general system of multi-sextic functional equations defining a multi-sextic mapping to a single equation. We also establish the Hyers-Ulam and Găvruţa stability of multi-sextic mappings by a fixed point theorem in non-Archimedean normed spaces. Moreover, we generalize some known stability results in the setting of quasi-𝛽-normed spaces. Using a characterization result, we indicate an example for the case that a multi-sextic mapping is non-stable.

• Annals of Clinical Neurophysiology
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• v.23 no.2
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• pp.69-81
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• 2021

Cortico-cortical evoked potential (CCEP) mapping is a rapidly developing method for visualizing the brain network and estimating cortical excitability. The CCEP comprises the early N1 component the occurs at 10-30 ms poststimulation, indicating anatomic connectivity, and the late N2 component that appears at < 200 ms poststimulation, suggesting long-lasting effective connectivity. A later component at 200-1,000 ms poststimulation can also appear as a delayed response in some studied areas. Such delayed responses occur in areas with changed excitability, such as an epileptogenic zone. CCEP mapping has been used to examine the brain connections causally in functional systems such as the language, auditory, and visual systems as well as in anatomic regions including the frontoparietal neocortices and hippocampal limbic areas. Task-based CCEPs can be used to measure behavior. In addition to evaluations of the brain connectome, single-pulse electrical stimulation (SPES) can reflect cortical excitability, and so it could be used to predict a seizure onset zone. CCEP brain mapping and SPES investigations could be applied both extraoperatively and intraoperatively. These underused electrophysiologic tools in basic and clinical neuroscience might be powerful methods for providing insight into measures of brain connectivity and dynamics. Analyses of CCEPs might enable us to identify causal relationships between brain areas during cortical processing, and to develop a new paradigm of effective therapeutic neuromodulation in the future.

• Kyungpook Mathematical Journal
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• v.47 no.1
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• pp.69-76
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• 2007

Let $f$ denote a mapping from an orthogonality space ($\mathcal{X}$, ${\bot}$) into a real Banach space $\mathcal{Y}$. In this paper, we prove the Hyers-Ulam-Rassias stability of the orthogonally cubic functional equations $f(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+12f(x)$ and $f(x+y+2z)+f(x+y-2z)+f(2x)+f(2y)=2f(x+y)+4f(x+z)+4f(x-z)+4f(y+z)+4f(y-z)$, where $x{\bot}y$, $y{\bot}z$, $x{\bot}z$.

• Journal of Biomedical Engineering Research
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• v.17 no.4
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• pp.525-534
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• 1996

We have developed a fast steady state free precession interferometry (SSFPI) technique which is useful for the fMRl (functional Magnetic Resonance Imaging). As is known, SSFP sequence with a suitable adjustment of Vadient (readeut) allows us to measure precession angle 6 which in tw relates to the field inhomogeneity. Combining the two pulses (known as FID and Echo) in FADE (Fast Acquisition Double Echo) sequence, for example, one can obtain the interference term which is directly related to the precession angle It has been known that a fast high resolution magnetic field mapping is possible by use of the modified FADE sequence or SSFPI, and we have attempted to use the SSFPI technique for the susceptibility-induced fMRl. When the method is applied to the susceptibility effect based functional magnetic resonance imaging (fMRl), it was found that the direct susceptibility effect measurement was possible without perturbations such as the backgrounds and inflow effect. In this paper, simulation results and experimental results obtained with 2.0 Tesla MRI system are presented.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.35C no.12
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• pp.1-12
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• 1998

In this paper, a design and implementation of VHDL-to-C mapping in the VHDL compiler back-end is described. The analyzed data in an intermediate format(IF), produced by the compiler front-end, is transformed into a C-code model of VHDL semantics by the VHDL-to-C mapper. The C-code model for VHDL semantics is based on a functional template, including declaration, elaboration, initialization and execution parts. The mapping is carried out by utilizing C mapping templates of 129 types classified by mapping units and functional semantics, and iterative algorithms, which are combined with terminal information, to produce C codes. In order to generate the C program, the C codes are output to the functional template either directly or by combining the higher mapping result with intermediate mapping codes in the data queue. In experiments, it is shown that the VHDL-to-C mapper could completely deal with the VHDL analyzed programs from the compiler front-end, which deal with about 96% of major VHDL syntactic programs in the Validation Suite. As for the performance, it is found that the code size of VHDL-to-C is less than that of interpreter and worse than direct code compiler of which generated code is increased more rapidly with the size of VHDL design, and that the VHDL-to-C timing overhead is needed to be improved by the optimized implementation of mapping mechanism.