NONLINEAR FUNCTIONAL ANALYSIS AND APPLICATIONS N F ONLINEAR UNCTIONAL A A NALYSIS AND PPLICATIONS V 2 OLUME YEOL JE CHO JONG KYU KIM AND SHIN MIN KANG EDITORS Nova Science Publishers, Inc. New York .
CONTENTS Preface . i Strong Convergence of Explicit Iteration Process for a Finite Family if Z-Operators in Normed Spaces . 1 Feng Gu Positive Solutions of Three-point Boundary Value Problems for Nonlinear Singular 2nth-Order Diferential Equations . 7 Jiqiang Jiang,Lishan Liu and Yonghong Wu Some Uniqueness Theorems of Nonlinear Fractional Defferential Equations . 17 Azizollah Babakhani A Surjectivity Theorem for Condensing Perturbations . 23 Changsun Choi and In-Sook Kim On Nonlinear (A,η)-Monotone Operator Inclusion Systems with Fuzzy Mappings in Hilbert Spaces . 29 Heng-you Lan Recent Development of M-Estimation in Nonparametric Spatial Regression . 43 Zhengyan Lin and Degui Li On Stability of Hybrid Dynamical Systems with Time Delay . 57 Xinzhi Liu Existence of Solutions for Fuzzy Quasi-Variational Inequalities with Concave Membership Functions by Tolerance Approach . 73 Zhi-bin Liu, Yeol Je Cho and Nan-jing Huang On Extended Grand Furuta Inequality and Furuta’s Question . 89 C.-S. Lin PM-Service Policy M/G/1 and G/M/1 Queueing Systems . 99 λ Sunggon Kim and Jongho Bae 1.
PREFACE On July 25∼28, 2007, “the 9-th International Conference on Nonlinear Functional Analysis and Applications” was held at Gyeongsang National University (GNU) and KyungnamUniversity(KU)bytheﬁnancialsupport oftheResearchInstitute ofNatural SciencesofGNU,theInstituteofBasicScienceResearchofKU,theKoreanMathematical Society,thePusan-KyongnamMathematicalSociety,NovaScience Publishers,Inc.,New York, and others.
In: Nonlinear Functional Analysis and Applications. Volume 2 © 2012 Nova Science Publishers, Inc. STRONG CONVERGENCE OF EXPLICIT ITERATION PROCESS FOR A FINITE FAMILY OF Z-OPERATORS IN NORMED SPACES Feng Gu1 Abstract. Thepurpose ofthispaper istoestablish astrongconvergence fortwo-step iterationscheme witherrors to acommon ﬁxed point fora ﬁnite familyofZ-operators in normed spaces. The results presented in this paper generalize and improve the corresponding results of T. Zamﬁrescu[T. Zamﬁrescu, Fixed point theorems in metric spaces, Archiv der Mathematik 23 (1972), 292–298] and Arif Raﬁq[Arif Raﬁq, Strong convergence of a modiﬁed implicit iteration process for a ﬁnite family of Z-operators 2006, ArticleID 10328, 1–6].
In: Nonlinear Functional Analysis and Applications. Volume 2 © 2012 Nova Science Publishers, Inc. STRONG CONVERGENCE OF EXPLICIT ITERATION PROCESS FOR A FINITE FAMILY OF Z-OPERATORS IN NORMED SPACES Feng Gu1 Abstract. Thepurpose ofthispaper istoestablish astrongconvergence fortwo-step iterationscheme witherrors to acommon ﬁxed point fora ﬁnite familyofZ-operators in normed spaces. The results presented in this paper generalize and improve the corresponding results of T. Zamﬁrescu[T. Zamﬁrescu, Fixed point theorems in metric spaces, Archiv der Mathematik 23 (1972), 292–298] and Arif Raﬁq[Arif Raﬁq, Strong convergence of a modiﬁed implicit iteration process for a ﬁnite family of Z-operators 2006, ArticleID 10328, 1–6].
6 FengGu ≤ ≥ { } α +γ 1 for all n 1, u is a bounded sequences in K satisfying the following n Pn n conditions: P ∞ ∞ (a) α = ; ∞n=1 n ∞ (b) γ < .
In: Nonlinear Functional Analysis and Applications. Volume 2 © 2012 Nova Science Publishers, Inc. POSITIVE SOLUTIONS OF THREE-POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR SINGULAR 2nth-ORDER DIFFERENTIAL EQUATIONS ∗ Jiqiang Jiang1, Lishan Liu1,2, and Yonghong Wu2 Abstract. Inthispaper,byusingtheupperandlowersolutionsmethodandtheﬁxed point theorems, the existence of positive solution for 2nth-order three-point boundary value problem is obtained. As an application, an example to demonstrate the applica- tion of our main results is given.
In: Nonlinear Functional Analysis and Applications. Volume 2 © 2012 Nova Science Publishers, Inc. POSITIVE SOLUTIONS OF THREE-POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR SINGULAR 2nth-ORDER DIFFERENTIAL EQUATIONS ∗ Jiqiang Jiang1, Lishan Liu1,2, and Yonghong Wu2 Abstract. Inthispaper,byusingtheupperandlowersolutionsmethodandtheﬁxed point theorems, the existence of positive solution for 2nth-order three-point boundary value problem is obtained. As an application, an example to demonstrate the applica- tion of our main results is given.
8 JiqiangJiang,LishanLiuandYonghongWu area of investigation in recent years (see [1-6] and the references therein). In the case of n = 1 and n = 2 (a = 0), the existence and multiplicity of positive solutions for BVP(1.1) have been widely studied by [9,10, 12]. When n is an arbitrary natural num- ber, boundary value problem has attracted considerable attention, for example, see [11, 13]. In particular, Yao [11] showed the existence of n symmetric positive solutions as f(t,x) is nondecreasing on x. Recently, Zhao [8] studied the following2n-order singular BVP: ( − ( 1)nu(2n)(t)=f(t,u(t)), 0<t<1, (1.2) ··· − u(2k)(0)=u(2k)(1)=0, k=0,1,2, ,n 1, ≥ × ∞ → ∞ − where n 2, and f : (0,1) (0,+ ) [0,+ ). The existence of C(2n 2)[0,1] and − C(2n 1)[0,1]positive solution for BVP(1.2) is obtained.