A FIXED POINT APPROACH TO THE CAUCHY-RASSIAS STABILITY OF GENERAL JENSEN TYPE QUADRATIC-QUADRATIC MAPPINGS

박춘길,M. Eshaghi Gordji,H. Khodaei 대한수학회 2010 대한수학회보 Vol.47 No.5

In this paper, we investigate the Cauchy-Rassias stability in Banach spaces and also the Cauchy-Rassias stability using the alternative fixed point for the functional equation:[수식]f(sx + ty 2+ rz) + f(sx + ty 2− rz) + f(sx − ty 2+ rz) + f(sx − ty 2− rz)= s2f(x) + t2f(y) + 4r2f(z)for any fixed nonzero integers s, t, r with r ≠ ±1.

On the quadratic mapping in generalized quasi-Banach spaces

박춘길,전길웅,Gang Lu 충청수학회 2006 충청수학회지 Vol.19 No.3

In this paper, we prove the Hyers{Ulam{Rassias sta-bility of the quadratic mapping in generalized quasi-Banach spaces,and of the quadratic mapping in generalized p-Banach spaces.

The Riesz theorem in linear $n$-normed spaces

박춘길,HahngYun Chu 충청수학회 2006 충청수학회지 Vol.19 No.2

We prove the Riesz theorem in linear $n$-normed spaces

Isomorphisms in quasi-Banach algebras

박춘길,안종수 대한수학회 2008 대한수학회보 Vol.45 No.1

Using the Hyers-Ulam-Rassias stability method, we inves-tigate isomorphisms in quasi-Banach algebras and derivations on quasi-Banach algebras associated with the CauchyJensen functional equation 2f(x + y/2+ z) = f(x) + f(y) + 2 f(z), which was introduced and investigated in [2, 17]. The concept of HyersUlamRassias stability originated from the Th. M. Rassias’ stability the-orem that appeared in the paper: On the stability of the linear mappingin Banach spaces, Proc. Amer. Math. Soc.72 (1978), 297-300. Further-more, isometries and isometric isomorphisms in quasi-Banach algebrasare studied.

LaFeO₃ 함량에 따른 (1-x)Bi_0.5(Na_0.78K_0.22)_0.5TiO₃-xLaFeO₃의 강유전, 압전 특성

박춘길,임지호,박정수,Park, Chun-Kil,Lim, Ji-Ho,Park, Jung-Soo 한국전기전자재료학회 2017 전기전자재료학회논문지 Vol.30 No.3

$(1-x)Bi_{0.5}(Na_{0.78}K_{0.22})_{0.5}TiO_3-xLaFeO_3$ ceramics were fabricated using a solid state reaction method. The microstructural, ferroelectric and piezoelectric properties were characterized using X-ray diffraction (XRD), scanning electron microscope (SEM), and polarization hysteresis loops (P-E). XRD results indicated that BNKT ceramic crystal structure modified by $LaFeO_3$ was transformed from a ferroelectric tetragonal to a non-polar pesudo-cubic phase with increased $LaFeO_3$ content. The improved piezoelectric properties resulted from the addition of $LaFeO_3$ up to 3 mol%. The $LaFeO_3$ 3mol% sample showed markedly improved piezoelectric and strain behaviors in comparison with pure BNKT ceramic.

Generalized quasi-Banach spaces and quasi-$(2;p)$-normed spaces

박춘길 충청수학회 2006 충청수학회지 Vol.19 No.2

In this paper, the notion of a generalized quasi-normed spaceis introduced and its completion is investigated.We introduce quasi-2-normed spaces and quasi-(2; p)-normed spaces, andinvestigate the properties of quasi-2-normed spaces and quasi-(2;p)-normedspaces.

LaFeO3 함량에 따른 (1-x)Bi0.5(Na0.78K0.22)0.5TiO3-xLaFeO3의 강유전, 압전 특성

박춘길,임지호,박정수 한국전기전자재료학회 2017 전기전자재료학회논문지 Vol.30 No.3

(1-x)Bi0.5(Na0.78K0.22)0.5TiO3-xLaFeO3 ceramics were fabricated using a solid state reaction method. Themicrostructural, ferroelectric and piezoelectric properties were characterized using X-ray diffraction (XRD), scanningelectron microscope (SEM), and polarization hysteresis loops (P-E). XRD results indicated that BNKT ceramiccrystal structure modified by LaFeO3 was transformed from a ferroelectric tetragonal to a non-polar pesudo-cubicphase with increased LaFeO3 content. The improved piezoelectric properties resulted from the addition of LaFeO3 upto 3 mol%. The LaFeO3 3mol% sample showed markedly improved piezoelectric and strain behaviors in comparisonwith pure BNKT ceramic. 본 연구에서는 고상법을 이용하여 (1-x)Bi0.5(Na0.78K0.22)0.5TiO3-xLaFeO3 조성의 시편을 제작하였다. 시편을 XRD와 SEM 그리고 P-E 장비를 이용하여 미세구조와 강유전성, 압전특성을 분석하였다. XRD의 결과를 통해 정방정계(tetragonal) 구조의 순수한 BNKT가 LaFeO3의 첨가량이 증가하면서 의사입방정(Pseudo-cubic)으로 상전이가 일어나는 것을 확인하였다. LaFeO3가 3mol 이었을 때 가장 우수한 압전특성을 보였다. 순수한 BNKT일 때 보다 LaFeO3가 3mol% 첨가 되었을 때 압전 특성과 변형률이 향상되었다.

Positive linear operators in C^*-algebras

박춘길,안종수 대한수학회 2009 대한수학회보 Vol.46 No.5

It is shown that every almost positive linear mapping h : A→ B of a Banach *-algebra A to a Banach *-algebra B is a positive linear operator when h(rx) = rh(x) (r > 1) holds for all x ∈ A, and that every almost linear mapping h : A → B of a unital C^*-algebra A to a unital C^*-algebra B is a positive linear operator when h(2^nu^*y) = h(2^nu)^*h(y) holds for all unitaries u ∈ A, all y ∈ A, and all n = 0, 1, 2, . . ., by using the Hyers-Ulam-Rassias stability of functional equations. Under a more weak condition than the condition as given above, we prove that every almost linear mapping h : A→ B of a unital C^*-algebra A to a unital C^*-algebra B is a positive linear operator. It is applied to investigate states, center states and center-valued traces. It is shown that every almost positive linear mapping h : A→ B of a Banach *-algebra A to a Banach *-algebra B is a positive linear operator when h(rx) = rh(x) (r > 1) holds for all x ∈ A, and that every almost linear mapping h : A → B of a unital C^*-algebra A to a unital C^*-algebra B is a positive linear operator when h(2^nu^*y) = h(2^nu)^*h(y) holds for all unitaries u ∈ A, all y ∈ A, and all n = 0, 1, 2, . . ., by using the Hyers-Ulam-Rassias stability of functional equations. Under a more weak condition than the condition as given above, we prove that every almost linear mapping h : A→ B of a unital C^*-algebra A to a unital C^*-algebra B is a positive linear operator. It is applied to investigate states, center states and center-valued traces.

d-ISOMETRIC LINEAR MAPPINGS IN LINEAR d-NORMED BANACH MODULES

박춘길,Themistocles M. Rassias 대한수학회 2008 대한수학회지 Vol.45 No.1

We prove the Hyers–Ulam stability of linear d-isometries in linear d-normed Banach modules over a unital C*-algebra and of linear isometries in Banach modules over a unital C*-algebra. The main purpose of this paper is to investigate d-isometric C*-algebra isomorphisms between linear d-normed C*-algebras and isometric C*-algebra isomorphisms between C*-algebras, and d-isometric Poisson C*-algebra isomorphisms between linear d-normed Poisson C*-algebras and isometric Poisson C*-algebra isomorphisms between Poisson C*-algebras. We moreover prove the Hyers–Ulam stability of their d-isometric homomorphisms and of their isometric homomorphisms. We prove the Hyers–Ulam stability of linear d-isometries in linear d-normed Banach modules over a unital C*-algebra and of linear isometries in Banach modules over a unital C*-algebra. The main purpose of this paper is to investigate d-isometric C*-algebra isomorphisms between linear d-normed C*-algebras and isometric C*-algebra isomorphisms between C*-algebras, and d-isometric Poisson C*-algebra isomorphisms between linear d-normed Poisson C*-algebras and isometric Poisson C*-algebra isomorphisms between Poisson C*-algebras. We moreover prove the Hyers–Ulam stability of their d-isometric homomorphisms and of their isometric homomorphisms.

에어로졸 증착법에 의해 제조된 PZT 막의 상변화와 전기적 특성

박춘길,강동균,이승희,공영민,정대용,Park, Chun-Kil,Kang, Dong-Kyun,Lee, Seung-Hee,Kong, Young-Min,Jeong, Dae-Yong 한국전기전자재료학회 2017 전기전자재료학회논문지 Vol.30 No.9

$Pb(Zr_{0.52}Ti_{0.48})O_3$ (PZT) films with a thickness of $5{\sim}10{\mu}m$ at the morphotropic phase boundary were fabricated by aerosol-deposition (AD), and their phase evolution and electrical properties were investigated. The microstructure of the AD PZT films revealed nanosized grains with a low crystallinity and a dense structure at room temperature. The AD PZT films showed a mixture of tetragonal and rhombohedral phases. The post-annealing temperature was varied to study the phase transition behavior. The crystallinity of the AD PZT films was enhanced by annealing at 450, 550, and $650^{\circ}C$ for 2 h. At $650^{\circ}C$, the tetragonal and rhombohedral phases reacted to form a bridge phase between the two phases. The polarization-electric field hysteresis loops of the AD PZT film annealed at $650^{\circ}C$ exhibited a smaller cohesive field and a lower slim hysteresis than the films annealed at 450 and $550^{\circ}C$.