• Honam Mathematical Journal
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• v.40 no.1
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• pp.199-210
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• 2018

In this paper we obtain some formulae for several sums of generalized Fibonacci numbers $U_n$ and generalized Lucas numbers $V_n$ and their dual forms $G_n$ and $H_n$ by using extensions of an interesting identity by A. R. Amini for Fibonacci numbers to these four kinds of generalizations and their first and second derivatives.

• East Asian mathematical journal
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• v.34 no.3
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• pp.265-285
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• 2018

The main purpose of this paper, by using the resolvent operator technique associated with randomly (A, ${\eta}$, m)-accretive operator is to establish an existence and convergence theorem for a class of system of random nonlinear equations with fuzzy mappings in Banach spaces. Our works are improvements and generalizations of the corresponding well-known results.

• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.179-186
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• 1999

In this paper, we define the Henstock-Stieltjes representable and nearly Henstock-Stieltjes representable operators for vector-valued function, which are the generalizations of Pettis representable operator and then study some properties of these operators.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.2
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• pp.229-253
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• 2016

As a generalization of (i, j)-weakly m-continuous functions [43], we introduce the notion of weakly M(i, j)-continuous functions and obtain many characterizations and some properties of the functions. We show that the function is a unified form of some functions between m-spaces and certain kinds of weakly continuous functions in bitopological spaces.

• Journal for History of Mathematics
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• v.20 no.4
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• pp.49-60
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• 2007

In this article, the concept of rigidity of smooth surfaces in the three dimensional Euclidean space which naturally arises in elementary geometry is introduced, and the natural process of the development of rigidity theory for compact surfaces and its generalizations are investigated.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.813-831
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• 2000

In recent years, the theory of Wiener-Hopf equations has emerged as a novel and innovative technique for developing efficient and powerful numerical methods for solving variational inequalities and complementarity problems. In this paper, we provide an account of some of the fundamental aspects of the Wiener-Hopf equations with major emphasis on the formulation, computational algorithms, various generalizations and their applications. We also suggest some open problems for further research with sufficient information and references.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.859-868
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• 2011

In this article, by considering error inequalities, we propose a new way to treat the Fej$\'{e}$r and Hermite-Hadamard inequalities involving n knots and m-th derivative on H$\"{o}$lder spaces. Moreover, some new related estimations are also given.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.479-491
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• 2008

In [4], the authors studied the Pascal matrix and the Stirling matrices of the first kind and the second kind via the Fibonacci matrix. In this paper, we consider generalizations of Pascal matrix, Fibonacci matrix and Pell matrix. And, by using Riordan method, we have factorizations of them. We, also, consider some combinatorial identities.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.597-606
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• 2007

The object of the present paper is to show quasi-Hadamard products of certain p-valent functions with negative coefficients in the open unit disc. Our results are the generalizations of the corresponding results due to Yaguchi et al. [10], Aouf and Darwish [3], Lee et al. [5] and Sekine and Owa [9].

• Journal of the Korean Mathematical Society
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• v.47 no.1
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• pp.29-40
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• 2010

In this paper, we study a generalization of the Banach space B($l_2$) of all bounded linear operators on $l_2$. Over this space, we present some reasonable ways to define Schatten-type classes which are generalizations of the classical Schatten classes of compact operators on $l_2$.