• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.1025-1031
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• 2017

We prove the uniqueness of solutions for the boundary value problem of certain nonlinear elliptic operators in the setting: Given any continuous function f on the p-harmonic boundary of a complete Riemannian manifold, there exists a unique solution of certain nonlinear elliptic operators, which is a limit of a sequence of solutions of the operators with finite energy in the sense of supremum norm, on the manifold taking the same boundary value at each p-harmonic boundary as that of f.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1171-1180
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• 2018

In this paper, we prove that boundedness with respect to metric balls of weighted composition operators from the Kim class and the Smirnov class to weighted Bloch type spaces is equivalent to metrical compactness of weighted composition operators between these spaces.

• East Asian mathematical journal
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• v.23 no.2
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• pp.135-149
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• 2007

In 1975, Wenger [4] determined the fine spectra of $Ces{\grave{a}}ro$ operator $C_1$ on c, the space of convergent sequences. In [7], the spectrum of the Rhaly operators on $c_0$ and c, under the assumption that ${lim}\limits_{n{\rightarrow}{\infty}}(n+1)a_n\;=\;L\;{\neq}\;0$, has been determined. In this paper the author determine the fine spectra of the Rhaly matrix $R_a$ as an operator on the space c, with the same assumption.

• ETRI Journal
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• v.31 no.2
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• pp.140-150
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• 2009

Although mutation testing is potentially powerful, it is a computationally expensive testing method. To investigate how we can reduce the cost of object-oriented mutation testing, we have conducted empirical studies on class mutation operators. We applied class mutation operators to 866 classes contained in six open-source programs. An analysis of the number and the distribution of class mutants generated and preliminary data on the effectiveness of some operators are provided. Our study shows that the overall number of class mutants is smaller than for traditional mutants, which offers the possibility that class mutation can be made practically affordable.

• East Asian mathematical journal
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• v.6 no.2
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• pp.133-144
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• 1990

In 1982, N. Miller [5] showed a weighted $L^p$ boundedness theorem for pseudo differential operators with symbols $S^0_{1.0}$. In this paper, we shall prove the pointwise estimates, in terms of the Fefferman, Stein sharp function and Hardy Littlewood maximal function, for pseudo differential operators with reduced symbols and show a weighted $L^p$-boundedness for pseudo differential operators with symbol in $S^m_{\rho,\delta}$, 0{$\leq}{\delta}{\leq}{\rho}{\leq}1$, ${\delta}{\neq}1$, ${\rho}{\neq}0$ and $m=(n+1)(\rho-1)$.

• The Pure and Applied Mathematics
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• v.14 no.2 s.36
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• pp.71-84
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• 2007

In this paper, we define the C-Stieltjes integral of the functions mapping an interval [a,b] into a Banach space X with respect to g on [a,b], and the C-Stieltjes representable operators for the vector-valued functions which are the generalizations of the Henstock-Stieltjes representable operators. Some properties of the C-Stieltjes operators and the convergence theorems of the C-Stieltjes integral are given.

• The Pure and Applied Mathematics
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• v.15 no.2
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• pp.111-120
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• 2008

A semi local convergence analysis is provided for Newton's method in a Banach space setting. The operators involved are only locally Holderian. We make use of a point-based approximation and center-Holderian hypotheses. This approach can be used to approximate solutions of equations involving nonsmooth operators.

• Korean Journal of Mathematics
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• v.27 no.3
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• pp.581-594
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• 2019

In this study a new generalization for operators of two parameters type of fractional in the unit disk is proposed. The fractional operators in this generalization are in the Srivastava-Owa sense. Concerning with the related applications, the generalized Gauss hypergeometric function is introduced. Further, some boundedness properties on Bloch space are also discussed.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.613-629
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• 2021

In this paper, we present and prove new existence and uniqueness fixed point theorems for vector operators having a mixed monotone property in partially ordered product Banach spaces. Our results extend and improve existing works on τ-φ-concave operators in the scalar case. As an application, we study the existence and uniqueness of positive solutions for systems of nonlinear Neumann boundary value problems.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.227-237
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• 2021

Opial inequality and its consequences are useful in establishing existence and uniqueness of solutions of initial and boundary value problems for differential and difference equations. In this paper we analyze Opial-type inequalities for convex functions. We have studied different versions of these inequalities for a generalized integral operator. Further difference of Opial-type inequalities are utilized to obtain generalized mean value theorems, which further produce various interesting derivations for fractional and conformable integral operators.