• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.989-1004
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• 2023

In this paper, we are motivated to evaluate and investigate the necessary conditions for the fractional Volterra Fredholm integro-differential equation involving the ς-Hilfer fractional derivative. The given problem is converted into an equivalent fixed point problem by introducing an operator whose fixed points coincide with the solutions to the problem at hand. The existence and uniqueness results for the given problem are derived by applying Krasnoselskii and Banach fixed point theorems respectively. Furthermore, we investigate the convergence of approximated solutions to the same problem using the modified Adomian decomposition method. An example is provided to illustrate our findings.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.17-33
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• 2017

We present a new local as well as a semilocal convergence analysis for Steffensen's method in order to locate fixed points of operators on a Banach space setting. Using more precise majorizing sequences we show under the same or less computational cost that our convergence criteria can be weaker than in earlier studies such as [1-13], [21, 22]. Numerical examples are provided to illustrate the theoretical results.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.293-309
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• 2011

The purpose of this article is to prove strong convergence theorems for weak relatively nonexpansive mapping which is firstly presented in this article. In order to get the strong convergence theorems for weak relatively nonexpansive mapping, the monotone CQ iteration method is presented and is used to approximate the fixed point of weak relatively nonexpansive mapping, therefore this article apply above results to prove the strong convergence theorems of zero point for maximal monotone operators in Banach spaces. Noting that, the CQ iteration method can be used for relatively nonexpansive mapping but it can not be used for weak relatively nonexpansive mapping. However, the monotone CQ method can be used for weak relatively nonexpansive mapping. The results of this paper modify and improve the results of S.Matsushita and W.Takahashi, and some others.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.16 no.4
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• pp.276-280
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• 2016

A fixed rate speech coder based on the filter bank and the non-uniform sampling technique is proposed. The non-uniform sampling is achieved by the detection of inflection points (IPs). A speech block is band passed by the filter bank, and the subband signals are processed by the IP detector, and the detected IP patterns are compared with entries of the IP database. For each subband signal, the address of the closest member of the database and the energy of the IP pattern are transmitted through channel. In the receiver, the decoder recovers the subband signals using the received addresses and the energy information, and reconstructs the speech via the filter bank summation. As results, the coder shows fixed data rate contrary to the existing speech coders based on the non-uniform sampling. Through computer simulation, the usefulness of the proposed technique is confirmed. The signal-to-noise ratio (SNR) performance of the proposed method is comparable to that of the uniform sampled pulse code modulation (PCM) below 20 kbps data rate.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.3
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• pp.336-341
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• 2004

This paper proposes an independent component analysis(ICA) of the fixed-point (FP) algorithm based on secant method and the kurtosis. The FP algorithm based on secant method is applied to improve the analysis speed and performance by simplifying the calculation process of the complex derivative in Newton method, the kurtosis is applied to cluster the components. The proposed ICA has been applied to the problems for separating the 6-mixed signals of 500 samples and 8-mixed images of $512{\times}512$ pixels, respectively. The experimental results show that the proposed ICA has always a fixed analysis sequence. The result can be solved the limit of conventional ICA based on secant method which has a variable sequence depending on the running of algorithm. Especially, the proposed ICA can be used for classifying and identifying the signals or the images.

• Journal of Sensor Science and Technology
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• v.18 no.2
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• pp.116-121
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• 2009

Pressure-controlled sodium heat pipe furnace was designed and fabricated, and its characteristics was investigated. Pressure control system was controlled within ${\pm}0.5\;Pa$ at 150 kPa and the stability of pressure was decreased to ${\pm}2.5\;Pa$, when the pressure-controlled system connected with the heat pipe. The melting curve of Ag fixed-point realized well by the adiabatic method using the pressure-controlled sodium heat pipe furnace and its accuracy showed ${\pm}2.27\;mK$ from the calculation of 20% to 80% at the plateau. The freezing curve of Ag fixed-point also realized and its plateau value was 2.23 mK lower than that of the melting curve.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.1
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• pp.1-5
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• 2003

We suggest Bisection method, Fixed point method and Newton's method for finding the intersection point of a nonparametric surface and a line in $R^3$ and apply ray-tracing in Color Picture Tube or Color Display Tube.

• Korean Journal of Mathematics
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• v.23 no.2
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• pp.231-248
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• 2015

In this paper, we solve the following quadratic $\rho$-functional inequalities ${\parallel}f(\frac{x+y+z}{2})+f(\frac{x-y-z}{2})+f(\frac{y-x-z}{2})+f(\frac{z-x-y}{2})-f(x)-x(y)-f(z){\parallel}\;(0.1)\\{\leq}{\parallel}{\rho}(f(x+y+z+)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-f(z)){\parallel}$ where $\rho$ is a fixed complex number with ${\left|\rho\right|}<\frac{1}{8}$, and ${\parallel}f(x+y+z)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-4f(z){\parallel}\;(0.2)\\{\leq}{\parallel}{\rho}(f(\frac{x+y+z}{2})+f(\frac{x-y-z}{2})+f(\frac{y-x-z}{2})+f(\frac{z-x-y}{2})-f(x)-f(y)-f(z)){\parallel}$ where $\rho$ is a fixed complex number with ${\left|\rho\right|}$ < 4. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic $\rho$-functional inequalities (0.1) and (0.2) in complex Banach spaces.

• The Pure and Applied Mathematics
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• v.27 no.1
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• pp.25-33
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• 2020

In this paper, we consider the following quadratic (ρ₁, ρ₂)-functional equation (0, 1) $$N(2f({\frac{x+y}{2}})+2f({\frac{x-y}{2}})-f(x)-f(y)-{\rho}_1(f(x+y)+f(x-y)-2f(x)-2f(y))-{\rho}_2(4f({\frac{x+y}{2}})+f(x-y)-f(x)-f(y)),t){\geq}{\frac{t}{t+{\varphi}(x,y)}}$$, where ρ₂ are fixed nonzero real numbers with ρ₂ ≠ 1 and 2ρ₁ + 2ρ₂≠ 1, in fuzzy normed spaces. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (ρ₁, ρ₂)-functional equation (0.1) in fuzzy Banach spaces.

• International Journal of Naval Architecture and Ocean Engineering
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• v.6 no.1
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• pp.175-185
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• 2014

This study presents the prediction of propagated wave profiles using the wave information at a fixed point. The fixed points can be fixed in either space or time. Wave information based on the linear wave theory can be expressed by Fredholm integral equation of the first kinds. The discretized matrix equation is usually an ill-conditioned system. Tikhonov regularization was applied to the ill-conditioned system to overcome instability of the system. The regularization parameter is calculated by using the L-curve method. The numerical results are compared with the experimental results. The analysis of the numerical computation shows that the Tikhonov regularization method is useful.