• 제목/요약/키워드: k-uniformly convex

검색결과 90건 처리시간 0.031초

FIXED POINTS OF A CERTAIN CLASS OF ASYMPTOTICALLY REGULAR MAPPINGS

  • Jung, Jong-Soo;Thakur, Balwant-Singh;Sahu, Daya-Ram
    • 대한수학회보
    • /
    • 제37권4호
    • /
    • pp.729-741
    • /
    • 2000
  • In this paper, we study in Banach spaces the existence of fixed points of asymptotically regular mapping T satisfying: for each x, y in the domain and for n=1, 2,…, $$\parallelT^nx-T^ny\parallel\leq$\leq$a_n\parallelx-y\parallel+b_n (\parallelx-T^nx\parallel+\parallely-T^ny\parallely)$$ where $a_n,\; b_n,\; C_n$ are nonnegative constants satisfying certain conditions. We also establish some fixed point theorems for these mappings in a Hibert space, in L(sup)p spaces, in Hardy space H(sup)p, and in Soboleve space $H^{k,p} for 1<\rho<\infty \; and \; k\geq0$. We extend results from papers [10], [11], and others.

  • PDF

Weak Laws of Large Numbers for Weighted Sums of Fuzzy Random Variables

  • Hyun, Young-Nam;Kim, Yun-Kyong;Kim, Young-Ju;Joo, Sang-Yeol
    • Communications for Statistical Applications and Methods
    • /
    • 제16권3호
    • /
    • pp.529-540
    • /
    • 2009
  • In this paper, we present some results on weak laws of large numbers for weighted sums of fuzzy random variables taking values in the space of fuzzy numbers of the real line R. We first give improvements of WLLN for weighted sums of convex-compactly uniformly integrable fuzzy random variables obtained by Joo and Hyun (2005). And then, we consider the case that the averages of expectations of fuzzy random variables converges. As results, WLLN for weighted sums of convexly tight or identically distributed case is obtained.

NEW HYBRID ALGORITHM FOR WEAK RELATIVELY NONEXPANSIVE MAPPING AND INVERSE-STRONGLY MONOTONE MAPPING IN BANACH SPACE

  • Zhang, Xin;Su, Yongfu;Kang, Jinlong
    • Journal of applied mathematics & informatics
    • /
    • 제29권1_2호
    • /
    • pp.87-102
    • /
    • 2011
  • The purpose of this paper is to prove strong convergence theorems for finding a common element of the set of fixed points of a weak relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping by a new hybrid method in a Banach space. We shall give an example which is weak relatively nonexpansive mapping but not relatively nonexpansive mapping in Banach space $l^2$. Our results improve and extend the corresponding results announced by Ying Liu[Ying Liu, Strong convergence theorem for relatively nonexpansive mapping and inverse-strongly-monotone mapping in a Banach space, Appl. Math. Mech. -Engl. Ed. 30(7)(2009), 925-932] and some others.

COMPOSITE IMPLICIT RANDOM ITERATIONS FOR APPROXIMATING COMMON RANDOM FIXED POINT FOR A FINITE FAMILY OF ASYMPTOTICALLY NONEXPANSIVE RANDOM OPERATORS

  • Banerjee, Shrabani;Choudhury, Binayak S.
    • 대한수학회논문집
    • /
    • 제26권1호
    • /
    • pp.23-35
    • /
    • 2011
  • In the present work we construct a composite implicit random iterative process with errors for a finite family of asymptotically nonexpansive random operators and discuss a necessary and sufficient condition for the convergence of this process in an arbitrary real Banach space. It is also proved that this process converges to the common random fixed point of the finite family of asymptotically nonexpansive random operators in the setting of uniformly convex Banach spaces. The present work also generalizes a recently established result in Banach spaces.

AN INVESTIGATION ON GEOMETRIC PROPERTIES OF ANALYTIC FUNCTIONS WITH POSITIVE AND NEGATIVE COEFFICIENTS EXPRESSED BY HYPERGEOMETRIC FUNCTIONS

  • Akyar, Alaattin;Mert, Oya;Yildiz, Ismet
    • 호남수학학술지
    • /
    • 제44권1호
    • /
    • pp.135-145
    • /
    • 2022
  • This paper aims to investigate characterizations on parameters k1, k2, k3, k4, k5, l1, l2, l3, and l4 to find relation between the class of 𝓗(k, l, m, n, o) hypergeometric functions defined by $$5_F_4\[{\array{k_1,\;k_2,\;k_3,\;k_4,\;k_5\\l_1,\;l_2,\;l_3,\;l_4}}\;:\;z\]=\sum\limits_{n=2}^{\infty}\frac{(k_1)_n(k_2)_n(k_3)_n(k_4)_n(k_5)_n}{(l_1)_n(l_2)_n(l_3)_n(l_4)_n(1)_n}z^n$$. We need to find k, l, m and n that lead to the necessary and sufficient condition for the function zF([W]), G = z(2 - F([W])) and $H_1[W]=z^2{\frac{d}{dz}}(ln(z)-h(z))$ to be in 𝓢*(2-r), r is a positive integer in the open unit disc 𝒟 = {z : |z| < 1, z ∈ ℂ} with $$h(z)=\sum\limits_{n=0}^{\infty}\frac{(k)_n(l)_n(m)_n(n)_n(1+\frac{k}{2})_n}{(\frac{k}{2})_n(1+k-l)_n(1+k-m)_n(1+k-n)_nn(1)_n}z^n$$ and $$[W]=\[{\array{k,\;1+{\frac{k}{2}},\;l,\;m,\;n\\{\frac{k}{2}},\;1+k-l,\;1+k-m,\;1+k-n}}\;:\;z\]$$.

ELLIPTIC BIRKHOFF'S BILLIARDS WITH $C^2$-GENERIC GLOBAL PERTURBATIONS

  • Kim, Gwang-Il
    • 대한수학회보
    • /
    • 제36권1호
    • /
    • pp.147-159
    • /
    • 1999
  • Tabanov investigated the global symmetric perturbation of the integrable billiard mapping in the ellipse [3]. He showed the nonintegrability of the Birkhoff billiard in the perturbed domain by proving that the principal separatrices splitting angle is not zero.In this paper, using the exact separatrix map of an one-degree-of freedom Hamiltoniam system with time periodic perturbation, we show the existence the stochastic layer including the uniformly hyperbolic invariant set which implies the nonintegrability near the separatrices of a Birkhoff's billiard in the domain bounded by $C^2$ convex simple curve constructed by the generic global perturbation of the ellipse.

  • PDF

STRONG CONVERGENCE THEOREMS FOR NONEXPANSIVE MAPPINGS AND INVERSE-STRONGLY-MONOTONE MAPPINGS IN A BANACH SPACE

  • Liu, Ying
    • East Asian mathematical journal
    • /
    • 제26권5호
    • /
    • pp.627-639
    • /
    • 2010
  • In this paper, we introduce a new iterative sequence finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then we show that the sequence converges strongly to a common element of two sets. Using this result, we consider the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse-strongly-monotone mapping, the fixed point problem and the classical variational inequality problem. Our results improve and extend the corresponding results announced by many others.

조직등가팬텀을 이용한 임상초음파 영상의 질에 관한 연구 - 제주도 내 병원을 중심으로 - (A Study on the Quality of Image of Ultrasound Using the Tissue-mimicking Phantom - in some hospitals jeju province)

  • 양정화;이경성
    • 대한방사선기술학회지:방사선기술과학
    • /
    • 제29권2호
    • /
    • pp.63-69
    • /
    • 2006
  • 초음파 영상의 질은 진단에 많은 영향을 끼친다. 양질의 영상이 항상 일정하게 유지되기 위해서는 QA(Quality Assurance) 프로그램을 가지고 주기적인 관리가 이루어져야 할 것이다. 본 논문은 임상에서의 QA 상황을 파악하는 첫 번째 단계로 실제 병원의 초음파 영상의 질을 살펴보고자 하였다. 이를 위해 인간의 생체등가물질로 된 팬텀을 이용하여 정상 환자를 스캔할 때와 같은 기준 값에서 가상의 낭포 및 고반사 신호의 구조물들이 몇 개가 보이는지 convex probe와 linear probe를 측정하여 비교하였다. convex probe에서는 정상 간과 비슷한 0.5 dB에서 vertical group, cystic masses, high contrast masses에서는 대부분 잘 보였으며 지방간과 비슷한 조건인 0.7 dB에서는 vertical group이 중간레벨에서, cystic masses와 high contrast masses에서는 대체로 모두 잘 보였다. linear probe에서의 vertical group은 0.5 dB에서 중간레벨만 잘 보였고 cystic masses와 high contrast masses는 두 개에서 네 개 보이는 것들이 고루 분포되었으나 하나도 보이는 않는 경우가 11건수나 되었다. 0.7 dB에서는 vertical group이 6개 이하가 보이는 것이 대부분 이었고 cystic masses와 high contrast masses에서도 두개에서 네 개 보이는 것들이 고루 분포되었고 하나도 보이는 않는 경우도 40건 있었다. 이로서 지방간과 같은 조건하에서는 linear probe의 영상의 질이 대체로 좋지 않으므로 기준 설정 및 물리적인 조건들을 검사 시에 잘 조정하거나 probe의 교체가 필요하다고 판단된다. 많은 병원에서 초음파 장비를 잘 관리하고 있다고 하지만, 영상의 질은 아직도 미흡한 것을 알 수 있다. 초음파 장비의 설치에서부터 영상의 질을 평가하고 지속적이고 정기적인 관리와 평가가 이루어질 수 있는 프로그램이 필요하겠다.

  • PDF

얕은터널에서 천단의 변형형태에 따른 그라운드 아칭에 관한 실험적 연구 (Experimental study on the ground arching depending on the deformation type of the crown in the shallow tunnel)

  • 임일재;이상덕
    • 한국터널지하공간학회 논문집
    • /
    • 제19권5호
    • /
    • pp.733-747
    • /
    • 2017
  • 터널을 굴착하면 터널주변과 상부의 지반이 느슨해지고 변형되며, 이로 인해 터널주변지반의 응력이 변화된다. Terzaghi는 터널굴착으로 인한 천단 상부지반의 이완형태를 Trapdoor 실험을 통해 규명하였다. 그러나 Terzaghi는 터널천단부가 등변위 되는 조건만 생각하였으며, 터널천단부가 오목곡선이나 볼록곡선 등의 형태로 변형될 경우에 대해서는 생각하지 않았다. 따라서 본 과제에서 지반이완 형태와 터널천단부 변위형태의 상관관계에 대하여 실험적으로 연구하였다. 이를 위하여 터널천단부의 이완형태를 등변위, 오목곡선, 볼록곡선의 세가지 형태로 모사하여 실험을 수행하고 그 결과를 비교 하였다. 실험결과 이완지반의 하중전이는 지반변형특성에 따라 다양한 형태로 발생될 수 있음을 확인하였다.

양극산화에 의한 티타늄 산화막의 표면 특성 및 생체 활성에 관한 연구 (SURFACE CHARACTERISTICS AND BIOACTIVITY OF ANODICALLY OXIDIZED TITANIUM SURFACES)

  • 이상한;조인호
    • 대한치과보철학회지
    • /
    • 제45권1호
    • /
    • pp.85-97
    • /
    • 2007
  • Statement of problem: Recently, anodic oxidation of cp-titanium is a popular method for treatment of titanium implant surfaces. It is a relatively easy process, and the thickness, structure, composition, and the microstructure of the oxide layer can be variably modified. Moreover the biological properties of the oxide layer can be controlled. Purpose: In this study, the roughness, microstructure, crystal structure of the variously treated groups (current, voltage, frequency, electrolyte, thermal treatment) were evaluated. And the specimens were soaked in simulated body fluid (SBF) to evaluate the effects of the surface characteristics and the oxide layers on the bioactivity of the specimens which were directly related to bone formation and integration. Materials and methods: Surface treatments consisted of either anodization or anodization followed thermal treatment. Specimens were divided into seven groups, depending on their anodizing treatment conditions: constant current mode (350V for group 2), constant voltage mode (155V for group 3), 60 Hz pulse series (230V for group 4, 300V for group 5), and 1000 Hz pulse series (400V for group 6, 460V for group 7). Non-treated native surfaces were used as controls (group 1). In addition, for the purpose of evaluating the effects of thermal treatment, each group was heat treated by elevating the temperature by $5^{\circ}C$ per minute until $600^{\circ}C$ for 1 hour, and then bench cured. Using scanning electron microscope (SEM), porous oxide layers were observed on treated surfaces. The crystal structures and phases of titania were identified by thin-film x-ray diffractmeter (TF-XRD). Atomic force microscope (AFM) was used for roughness measurement (Sa, Sq). To evaluate bioactivity of modified titanium surfaces, each group was soaked in SBF for 168 hours (1 week), and then changed surface characteristics were analyzed by SEM and TF-XRD. Results: On basis of our findings, we concluded the following results. 1. Most groups showed morphologically porous structures. Except group 2, all groups showed fine to coarse convex structures, and the groups with superior quantity of oxide products showed superior morphology. 2. As a result of combined anodization and thermal treatment, there were no effects on composition of crystalline structure. But, heat treatment influenced the quantity of formation of the oxide products (rutile / anatase). 3. Roughness decreased in the order of groups 7,5,2,3,6,4,1 and there was statistical difference between group 7 and the others (p<0.05), but group 7 did not show any bioactivity within a week. 4. In groups that implanted ions (Ca/P) on the oxide layer through current and voltage control, showed superior morphology, and oxide products, but did not express any bioactivity within a week. 5. In group 3, the oxide layer was uniformly organized with rutile, with almost no titanium peak. And there were abnormally more [101] orientations of rutile crystalline structure, and bonelike apatite formation could be seen around these crystalline structures. Conclusion: As a result of control of various factors in anodization (current, voltage, frequency, electrolytes, thermal treatment), the surface morphology, micro-porosity, the 2nd phase formation, crystalline structure, thickness of the oxide layer could be modified. And even more, the bioactivity of the specimens in vitro could be induced. Thus anodic oxidation can be considered as an excellent surface treatment method that will able to not only control the physical properties but enhance the biological characteristics of the oxide layer. Furthermore, it is recommended in near future animal research to prove these results.