• International Journal of Computer Science & Network Security
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• 제24권1호
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• pp.85-94
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• 2024

In this paper, we present the very first time the generalized notion of (α, β, γ, δ) - convex (concave) function in mixed kind, which is the generalization of (α, β) - convex (concave) functions in 1^st and 2^nd kind, (s, r) - convex (concave) functions in mixed kind, s - convex (concave) functions in 1^st and 2^nd kind, p - convex (concave) functions, quasi convex(concave) functions and the class of convex (concave) functions. We would like to state the well-known Ostrowski inequality via SVN-Riemann Integrals for (α, β, γ, δ) - convex (concave) function in mixed kind. Moreover we establish some SVN-Ostrowski type inequalities for the class of functions whose derivatives in absolute values at certain powers are (α, β, γ, δ)-convex (concave) functions in mixed kind by using different techniques including Hölder's inequality and power mean inequality. Also, various established results would be captured as special cases with respect to convexity of function.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권1호
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• pp.49-57
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• 2018

We have introduced two new notions of convexity and closedness in functional analysis. Let X be a real normed space, then $C({\subseteq}X)$ is functionally convex (briefly, F-convex), if $T(C){\subseteq}{\mathbb{R}}$ is convex for all bounded linear transformations $T{\in}B$(X, R); and $K({\subseteq}X)$ is functionally closed (briefly, F-closed), if $T(K){\subseteq}{\mathbb{R}}$ is closed for all bounded linear transformations $T{\in}B$(X, R). By using these new notions, the Alaoglu-Bourbaki-Eberlein-${\check{S}}muljan$ theorem has been generalized. Moreover, we show that X is reflexive if and only if the closed unit ball of X is F-closed. James showed that for every closed convex subset C of a Banach space X, C is weakly compact if and only if every $f{\in}X^{\ast}$ attains its supremum over C at some point of C. Now, we show that if A is an F-convex subset of a Banach space X, then A is bounded and F-closed if and only if every element of $X^{\ast}$ attains its supremum over A at some point of A.

• 한국정보과학회논문지:컴퓨팅의 실제 및 레터
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• 제9권6호
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• pp.712-717
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• 2003

자연배경으로부터 불특정 다수 객체의 윤곽선들을 자동 추출하는 다중 스네이크(Snake) 알고리즘을 제안하였다. 먼저 잡음에 강건한 문맥자유 주목연산자(context-free attention operator)를 이용하여 자연배경에 혼재하는 불특정 다수 객체들을 자동 검출하고, 각 객체별로 스네이크의 초기 윤곽들을 자동 설정함으로써 기존 스네이크 알고리즘에서는 어려웠던 초기 윤곽의 자동 설정과 여러 객체 윤곽선의 동시 추출 문제를 해결하였다. 이때 각 스네이크의 초기 윤곽들은 기존의 방법들에 비해 객체들의 실제윤곽선에 좀 더 가까이 설정하여 요철이 큰 객체들의 윤곽선도 쉽게 추출 할 수 있도록 하였다. 다양한 합성 영상과 자연배경의 실영상에 대해 실험하여 잡음이 있는 복잡한 배경으로부터도 불특정 다수 객체의 윤곽선을 효과적으로 자동 추출함을 확인하였다.