• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제22권2호
• /
• pp.185-197
• /
• 2015

The author considers a Noor-type iterative scheme to approximate com- mon fixed points of an infinite family of uniformly quasi-sup(f_n)-Lipschitzian map- pings and an infinite family of g_n-expansive mappings in convex cone metric spaces. His results generalize, improve and unify some corresponding results in convex met- ric spaces [1, 3, 9, 16, 18, 19] and convex cone metric spaces [8].

• 대한수학회논문집
• /
• 제17권1호
• /
• pp.37-51
• /
• 2002

Let X be a reflexive Banach space with a uniformly Gateaux differentiable norm, C a nonempty bounded open subset of X, and T a continuous mapping from the closure of C into X which is locally pseudo-contractive mapping on C. We show that if the closed unit ball of X has the fixed point property for nonexpansive self-mappings and T satisfies the following condition: there exists z $\in$ C such that ∥z-T(z)∥<∥x-T(x)∥ for all x on the boundary of C, then the trajectory tlongrightarrowz$_{t}$$\in$C, t$\in$[0, 1) defined by the equation z$_{t}$ = tT(z$_{t}$)+(1-t)z is continuous and strongly converges to a fixed point of T as t longrightarrow 1￣.ow 1￣.

• 대한수학회논문집
• /
• 제28권2호
• /
• pp.243-267
• /
• 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.

• 대한수학회지
• /
• 제52권5호
• /
• pp.1023-1036
• /
• 2015

Let {Xn; $n{\succeq}1$} be a field of martingale differences taking values in a p-uniformly smooth Banach space. The paper provides conditions under which the series ${\sum}_{i{\preceq}n}\;Xi$ converges almost surely and the tail series {$Tn={\sum}_{i{\gg}n}\;X_i;n{\succeq}1$} satisfies $sup_{k{\succeq}n}{\parallel}T_k{\parallel}=\mathcal{O}p(b_n)$ and ${\frac{sup_{k{\succeq}n}{\parallel}T_k{\parallel}}{B_n}}{\rightarrow\limits^p}0$ for given fields of positive numbers {bn} and {Bn}. This result generalizes results of A. Rosalsky, J. Rosenblatt [7], [8] and S. H. Sung, A. I. Volodin [11].

• Kyungpook Mathematical Journal
• /
• 제60권3호
• /
• pp.629-645
• /
• 2020

A uniformly convergent numerical method is developed for solving singularly perturbed 1-D parabolic convection-diffusion problems. The developed method applies a non-standard finite difference method for the spatial derivative discretization and uses the implicit Runge-Kutta method for the semi-discrete scheme. The convergence of the method is analyzed, and it is shown to be first order convergent. To validate the applicability of the proposed method two model examples are considered and solved for different perturbation parameters and mesh sizes. The numerical and experimental results agree well with the theoretical findings.

• Nonlinear Functional Analysis and Applications
• /
• 제26권3호
• /
• pp.451-474
• /
• 2021

In this paper, we investigate a hybrid algorithm for finding zeros of the sum of maximal monotone operators and Lipschitz continuous monotone operators which is also a common fixed point problem for finite family of relatively quasi-nonexpansive mappings and split feasibility problem in uniformly convex real Banach spaces which are also uniformly smooth. The iterative algorithm employed in this paper is design in such a way that it does not require prior knowledge of operator norm. We prove a strong convergence result for approximating the solutions of the aforementioned problems and give applications of our main result to minimization problem and convexly constrained linear inverse problem.

• 대한수학회지
• /
• 제46권4호
• /
• pp.827-840
• /
• 2009

Let {$X_{ni}$ | $1{\leq}i{\leq}n,\;n{\geq}1$} be an array of rowwise negatively dependent (ND) random variables. We in this paper discuss the conditions of ${\sum}^n_{t=1}a_{ni}X_{ni}{\rightarrow}0$ completely as $n{\rightarrow}{\infty}$ under not necessarily identically distributed setting and the strong law of large numbers for weighted sums of arrays of rowwise negatively dependent random variables is also considered.

• 한국세라믹학회지
• /
• 제51권4호
• /
• pp.357-361
• /
• 2014

An Ni-Fe/YSZ core-shell structured anode for uniform microstructure and catalytic activity was synthesized. Flat tubular segmented-in-series solid oxide fuel cell-stacks were prepared by decalcomania method using synthesized anode powder. The Ni-Fe/YSZ core-shell anode exhibited better electrical conductivity than a commercially available Ni-YSZ cermet anode. Also power output increased by 1.3 times with a higher open circuit voltage. These results can be attributed to the uniformly distributed Ni particles in the YSZ framework. The impedance spectra of a Ni-Fe/YSZ core-shell anode showed comparable reduced ohmic resistance similar to those of the commercially available Ni-YSZ cermet anodes.

• Journal of applied mathematics & informatics
• /
• 제39권3_4호
• /
• pp.419-435
• /
• 2021

This paper deals with numerical treatment of singularly perturbed differential equations involving small delays. The highest order derivative in the equation is multiplied by a perturbation parameter 𝜀 taking arbitrary values in the interval (0, 1]. For small 𝜀, the problem involves a boundary layer of width O(𝜀), where the solution changes by a finite value, while its derivative grows unboundedly as 𝜀 tends to zero. The considered problem contains delay on the convection and reaction terms. The terms with the delays are approximated using Taylor series approximations resulting to asymptotically equivalent singularly perturbed BVPs. Inducing exponential fitting factor for the term containing the singular perturbation parameter and using central finite difference for the derivative terms, numerical scheme is developed. The stability and uniform convergence of difference schemes are studied. Using a priori estimates we show the convergence of the scheme in maximum norm. The scheme converges with second order of convergence for the case 𝜀 = O(N^-1) and for the case 𝜀 ≪ N^-1, the scheme converge uniformly with first order of convergence, where N is number of mesh intervals in the domain discretization. We compare the accuracy of the developed scheme with the results in the literature. It is found that the proposed scheme gives accurate result than the one in the literatures.

• 융복합기술연구소 논문집
• /
• 제6권2호
• /
• pp.35-40
• /
• 2016

Ignitor tip is a component of burner to start the burning process in power plant. This is used to ignite the coal to a constant operating state by fuel mixed with air and kerosene. This component is composed of three components so that air and kerosene are mixed in the proper ratio and injected uniformly. Because the parts with the designed shape are manufactured in the machining process, they have to be made of three parts. These parts are designed to have various functions in each part. The mixing part mixes the supplied air and kerosene through the six holes and sends it to the injecting part at the proper ratio. The inject part injects mixed fuel, which is led to have a constant rotational direction in the connecting part, to the burner. And the connecting plate that the mixed fuel could rotate and spray is assembled so that the flame can be injected uniformly. But this part causes problems that are worn by vibration and rotation because it is mechanically assembled between the mixing part and the inject part. In this study, 3D printing method is used to integrate a connecting plate and an inject part to solve this wear problem. The 3D printing method could make this integrated part because the process is carried out layer by layer using a metal powder material. The part manufactured by 3D printing process should perform the post process such as support removal and surface treatment. However, while performing the 3D printing process, the material properties of the metal powders are changed by the laser sintering process. This change in material properties makes the post process difficult. In consideration of these variables, we have studied the optimization of manufacturing process using 3D printing method.