• Korean Journal of Mathematics
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• 제24권2호
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• pp.169-179
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• 2016

In this article, we introduce the concept of ordered dualistic partial metric spaces and establish an order relation on quasi dualistic partial metric spaces. Later on, using this order relation, we prove xed point theorems for single and multivalued mappings. We support our results with some illustrative examples.

• East Asian mathematical journal
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• 제25권2호
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• pp.141-146
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• 2009

In this paper, we introduce a new generalized nonlinear quasivariational inequality and establish its equivalence with a xed point problem by using the resolvent operator technique. Utilizing this equivalence, we suggest two iterative schemes, prove two existence theorems of solutions for the generalized nonlinear quasivariational inequality involving generalized cocoercive mapping and establish some convergence results of the sequences generated by the algorithms. Our results include several previously known results as special cases.

• 한국표면공학회:학술대회논문집
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• 한국표면공학회 2016년도 추계학술대회 논문집
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• pp.176-176
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• 2016

마이크로 블레이드 제조를 위한 기초 연구로서, 전기도금 방법을 이용하여 Ni 및 다이아몬드 분말을 복합도금을 시켰다. $15{\sim}25{\mu}m$ 크기 분포를 갖는 다이아몬드 분말 농도 변화에 따라 전착되는 다이아몬드 분포 및 전기도금 용액 내 Ni 농도 변화에 따라 전착되는 다이아몬드 분포를 관찰하였다. 이를 위하여 광학현미경, 전자현미경(SEM), EDS 및 XED를 이용하였다. Ni 농도 변화보다는 다이아몬드 분말 농도 변화가 전착되는 다이아몬드 분포에 더 큰 영향을 미침을 알 수 있었다.

• 대한수학회보
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• 제48권3호
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• pp.575-584
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• 2011

In Shahzad and Zegeye [Nonlinear Anal. 71 (2009), no. 3-4, 838-844], the authors introduced several Ishikawa iterative schemes for xed points of multi-valued mappings in Banach spaces, and proved some strong convergence theorems by using their iterations. In their proofs of the main results, it seems reasonable and simpler to prove for the iteration {$x_n$} to be a Cauchy sequence. In this paper, we modify and improve the proofs of the main results given by Shahzad and Zegeye. Two concrete examples also are given.

• Korean Journal of Mathematics
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• 제24권1호
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• pp.81-106
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• 2016

In this paper, we study the fractional iterates of the exponential function. This is an unresolved problem, not due to a lack of a known solution, but because there are an innite number of solutions, and there is no agreement as to which solution is "best." We will approach the problem by rst solving Abel's functional equation ${\alpha}(e^x)={\alpha}(x)+1$ by perturbing the exponential function so as to produce a real xed point, allowing a unique holomorphic solution. We then use this solution to nd a solution to the unperturbed problem. However, this solution will depend on the way we rst perturbed the exponential function. Thus, we then strive to remove the dependence of the perturbed function. Finally, we produce a solution that is in a sense more natural than other solutions.

• East Asian mathematical journal
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• 제24권2호
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• pp.177-186
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• 2008

In this paper, we introduce and study a new class of system of parametric general quasivariational-like inequalities. Using $\eta$-subdifferential and $\eta$-proximal mappings of proper functionals in Hilbert spaces, we prove the equivalence between the system of parametric general quasivariational-like inequalities and a xed point problem and construct two iterative algorithms. A few existence and uniqueness results as well as the sensitivity analysis of solutions are also established for the system of parametric general quasivariational-like inequalities, and some convergence results of iterative sequence generated by the algorithms are proved. Our results extend a few known results in the literature.

• Journal of the Korean Data and Information Science Society
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• 제21권3호
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• pp.561-567
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• 2010

Multiclassification is typically performed using voting scheme methods based on combining a set of binary classifications. In this paper we use multiclassification method with a hat matrix of least squares support vector machine (LS-SVM), which can be regarded as the revised one-against-all method. To tackle multiclass problems for large data, we use the $Nystr\ddot{o}m$ approximation and the quadratic Renyi entropy with estimation in the primal space such as used in xed size LS-SVM. For the selection of hyperparameters, generalized cross validation techniques are employed. Experimental results are then presented to indicate the performance of the proposed procedure.

• Kyungpook Mathematical Journal
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• 제50권2호
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• pp.315-327
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• 2010

We give a xed point approach to the generalized Hyers-Ulam stability of the cubic equation f(2x + y) + f(2x - y) = 2f(x + y) + 2f(x - y) + 12f(x) in non-Archimedean normed spaces. We will give an example to show that some known results in the stability of cubic functional equations in real normed spaces fail in non-Archimedean normed spaces. Finally, some applications of our results in non-Archimedean normed spaces over p-adic numbers will be exhibited.

• Kyungpook Mathematical Journal
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• 제56권2호
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• pp.397-408
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• 2016

Let R be a 2-torsion free prime ring with center Z, U be the Utumi quotient ring, Q be the Martindale quotient ring of R, d be a derivation of R and L be a Lie ideal of R. If $d(uv)^n=d(u)^md(v)^l$ or $d(uv)^n=d(v)^ld(u)^m$ for all $u,v{\in}L$, where m, n, l are xed positive integers, then $L{\subseteq}Z$. We also examine the case when R is a semiprime ring. Finally, as an application we apply our result to the continuous derivations on non-commutative Banach algebras. This result simultaneously generalizes a number of results in the literature.

• East Asian mathematical journal
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• 제25권1호
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• pp.11-26
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• 2009

In this paper, the concepts of compatible mappings of types (A) and (P) are introduced in an induced metric space, two common xed point theorems for two pairs of compatible mappings of types (A) and (P) in an induced complete metric space are established. As their applications, the existence and uniqueness results of common solution for a system of functional equations arising in dynamic programming are discussed.