• Journal of applied mathematics & informatics
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• 제42권1호
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• pp.1-14
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• 2024

Let G = (V, E) be a (p, q) graph. Define $$\begin{cases}\frac{p}{2},\:if\:p\:is\:even\\\frac{p-1}{2},\:if\:p\:is\:odd\end{cases}$$ and L = {±1, ±2, ±3, ···, ±ρ} called the set of labels. Consider a mapping f : V → L by assigning different labels in L to the different elements of V when p is even and different labels in L to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd.The labeling as defined above is said to be a pair difference cordial labeling if for each edge uv of G there exists a labeling |f(u) - f(v)| such that |Δ_f1 - Δ_f^c1| ≤ 1, where Δ_f1 and Δ_f^c1 respectively denote the number of edges labeled with 1 and number of edges not labeled with 1. A graph G for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate the pair difference cordial labeling behavior of subdivision of some graphs.

• 대한수학회보
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• 제39권2호
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• pp.333-346
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• 2002

Let $F={F^v:S^1->S^1,v\in\; V$ and $g={G^v:S^1->S^1,v\in\; V$ be disjoint flows defined on the unit circle $S^1$, that is such flows that each their element either is the identity mapping or has no fixed point ((V, +) is a 2-divisible nontrivial abelian group). The aim of this paper is to give a necessary and sufficient codition for topological conjugacy of disjoint flows i.e., the existence of a homeomorphism $\Gamma:S^1->S^1$ satisfying $$\Gamma\circ\ F^v=G^v\circ\Gamma,\; v\in\; V$$ Moreover, under some further restrictions, we determine all such homeomorphisms.

• East Asian mathematical journal
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• 제24권1호
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• pp.81-95
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• 2008

Let E be a uniformly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm, C a nonempty closed convex subset of E, and $T\;:\;C\;{\rightarrow}\;E$ a nonexpansive mapping satisfying the weak inwardness condition. Assume that every weakly compact convex subset of E has the fixed point property. For $f\;:\;C\;{\rightarrow}\;C$ a contraction and $t\;{\in}\;(0,\;1)$, let $x_t$ be a unique fixed point of a contraction $T_t\;:\;C\;{\rightarrow}\;E$, defined by $T_tx\;=\;tf(x)\;+\;(1\;-\;t)Tx$, $x\;{\in}\;C$. It is proved that if {$x_t$} is bounded, then $x_t$ converges to a fixed point of T, which is the unique solution of certain variational inequality. Moreover, the strong convergence of other implicit and explicit iterative schemes involving the sunny nonexpansive retraction is also given in a reflexive and strictly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm.

• 대한수학회지
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• 제52권4호
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• pp.699-725
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• 2015

In this paper, we study the estimation for algebraic polynomials in the bounded and unbounded regions bounded by piecewise Dini smooth curve having interior and exterior zero angles.

• 전자공학회논문지B
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• 제29B권7호
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• pp.87-97
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• 1992

Fuzzy controllers have been successfully applied to many cases to which conventional control algorithms are difficult to be applied. Even though the representations and the processings of data and information in the fuzzy controller are quite different from those in other control algorithms, the information processing operation that it caries out is basically a function ∫: $A{\subset}R^n{\to}R^m$, from a bounded subset A of an n-dimensional Euclidean space to a bounded subset f[A] of an m-dimensional Euclidean space, where n and m are the number of measured states and the number of control inputs of the controlled system, respectively. Under the assumptions of Mamdani's direct reasoning method and C.O.G.(center of gravity) defuzzification method, the fuzzy controllers are proven to perform the mapping of any given functions f with appropriately defined fuzzy sets. The mapping capabilities of fuzzy controllers are analyzed in detail for two cases, ∫: $R^{1}{\to}R^{1}$ and g: $R^{2}{\to}R^{1}$. Also, it will be shown that the results can be extended to multiple dimensional cases.

• 대한수학회보
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• 제55권6호
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• pp.1783-1789
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• 2018

This paper treats the class of normalized logharmonic mappings $f(z)=zh(z){\overline{g(z)}}$ in the unit disk satisfying ${\varphi}(z)=zh(z)g(z)$ is analytically typically real. Every such mapping f admits an integral representation in terms of its second dilatation function and a function of positive real part with real coefficients. The radius of starlikeness and an upper estimate for arclength are obtained. Additionally, it is shown that f maps the unit disk into a domain symmetric with respect to the real axis when its second dilatation has real coefficients.

• 대한수학회논문집
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• 제23권2호
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• pp.191-199
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• 2008

We investigate the relation between the vector variable bi-additive functional equation $f(\sum\limits^n_{i=1} xi,\;\sum\limits^n_{i=1} yj)={\sum\limits^n_{i=1}\sum\limits^n_ {j=1}f(x_i,y_j)$ and the multi-variable quadratic functional equation $$g(\sum\limits^n_{i=1}xi)\;+\;\sum\limits_{1{\leq}i<j{\leq}n}\;g(x_i-x_j)=n\sum\limits^n_{i=1}\;g(x_i)$$. Furthermore, we find out the general solution of the above two functional equations.

• East Asian mathematical journal
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• 제32권5호
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• pp.701-716
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• 2016

We establish a tripled coincidence and common tripled fixed point theorem for hybrid pair of mappings satisfying new contractive condition. To find tripled coincidence points, we do not use the continuity of any mapping involved therein. An example is also given to validate our result. We improve, extend and generalize several known results.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제27권3호
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• pp.109-124
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• 2020

We establish coincidence point theorem for S-non-decreasing mappings under Geraghty-type contraction on partially ordered metric spaces. With the help of obtain result, we derive two dimensional results for generalized compatible pair of mappings F, G : X² → X. As an application, we obtain the solution of integral equation and also give an example to show the usefulness of our results. Our results improve, sharpen, enrich and generalize various known results.

• Kyungpook Mathematical Journal
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• 제52권1호
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• pp.33-38
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• 2012

The purpose of the present paper is to investigate mapping properties of an integral operator in which we show that the function g defined by $$g(z)=\{\frac{c+{\alpha}}{z^c}{\int}_{o}^{z}t^{c-1}(D^nf)^{\alpha}(t)dt\}^{1/{\alpha}}$$. belongs to the class $S(A,B)$ if $f{\in}S(n,A,B)$.