In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park （Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7（2000）, 1-28） to obtain an a...In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park （Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7（2000）, 1-28） to obtain an almost fixed point theorem for upper [resp., lower] semicontinuous multimaps in locally G-convex spaces, and then give a fixed point theorem for upper semicontinuous multimap with closed Γ-convex values.展开更多
In this paper, some results on the upper convex densities of self-similar sets at the contracting-similarity fixed points are discussed. Firstly, a characterization of the upper convex densities of self-similar sets a...In this paper, some results on the upper convex densities of self-similar sets at the contracting-similarity fixed points are discussed. Firstly, a characterization of the upper convex densities of self-similar sets at the contracting-similarity fixed points is given. Next, under the strong separation open set condition, the existence of the best shape for the upper convex densities of self-similar sets at the contracting-similarity fixed points is proven. As consequences, an open problem and a conjecture, which were posed by Zhou and Xu, are answered.展开更多
Based on the classical(matrix type)input-output analysis,a type of nonlinear (continuous type) conditional Leontief model,input-output equation were introduced,as well as three corresponding questions,namely,solvabili...Based on the classical(matrix type)input-output analysis,a type of nonlinear (continuous type) conditional Leontief model,input-output equation were introduced,as well as three corresponding questions,namely,solvability,continuity and surjectivity,and some fixed point and surjectivity methods in nonlinear analysis were used to deal with these questions. As a result,the main theorems are obtained,which provide some sufficient criterions to solve above questions described by the boundary properties of the enterprises consuming operator.展开更多
In this paper, using the context of complete partial metric spaces, some common fixed point results of maps that satisfy the generalized （ψ, Ф）-weak contractive conditions are obtained. Our results generalize, ext...In this paper, using the context of complete partial metric spaces, some common fixed point results of maps that satisfy the generalized （ψ, Ф）-weak contractive conditions are obtained. Our results generalize, extend, unify, enrich and complement many existing results in the literature. Example are given showing the validaty of our results.展开更多
The purpose of this paper is to obtain a generalization of the famous Browder's fixed point theorem and some equivalent forms. As application, these results are utilized to study the existence problems of fixed po...The purpose of this paper is to obtain a generalization of the famous Browder's fixed point theorem and some equivalent forms. As application, these results are utilized to study the existence problems of fixed points and nearest points.展开更多
We obtain some theorems for real increasing functions showing that elementary fixed point theory can bring to astonishing results by assuming only a few properties, some of which intrinsically possessed from these fun...We obtain some theorems for real increasing functions showing that elementary fixed point theory can bring to astonishing results by assuming only a few properties, some of which intrinsically possessed from these functions. An application is given for a theorem of quasi-compactness and a known result in posets is also recalled and applied to real intervals.展开更多
In this work, we will discuss Caristi’s fixed point theorem for mapping results introduced in the setting of normed spaces. This work is a generalization of the classical Caristi’s fixed point theorem. Also, Caristi...In this work, we will discuss Caristi’s fixed point theorem for mapping results introduced in the setting of normed spaces. This work is a generalization of the classical Caristi’s fixed point theorem. Also, Caristi’s type of fixed points theorem was partial discussed in Reich, Mizoguchi and Takahashi’s and Amini-Harandi’s results, we developed ideas that many known fixed point theorems can easily be derived from the Caristi theorem.展开更多
This paper aims at treating a study of Banach fixed point theorem for mapping results that introduced in the setting of normed space. The classical Banach fixed point theorem is a generalization of this work. A fixed ...This paper aims at treating a study of Banach fixed point theorem for mapping results that introduced in the setting of normed space. The classical Banach fixed point theorem is a generalization of this work. A fixed point theory is a beautiful mixture of Mathematical analysis to explain some conditions in which maps give excellent solutions. Here later many mathematicians used this fixed point theory to establish their results, see for instance, Picard-Lindel of Theorem, The Picard theorem, Implicit function theorem etc. Also, we developed ideas that many of known fixed point theorems can easily be derived from the Banach theorem. It extends some recent works on the extension of Banach contraction principle to metric space with norm spaces.展开更多
We prove some fixed point theorems in partially ordered sets, providing an extension of the Banach contractive mapping theorem. Having studied previously the nondecreasing case, we consider in this paper nonincreasing...We prove some fixed point theorems in partially ordered sets, providing an extension of the Banach contractive mapping theorem. Having studied previously the nondecreasing case, we consider in this paper nonincreasing mappings as well as non monotone mappings. We also present some applications to first-order ordinary differential equations with periodic boundary conditions, proving the existence of a unique solution admitting the existence of a lower solution.展开更多
In this paper, the fixed point theorems of composite set-valued increasing operators are given. As a corollary, the fixed point theorem for increasing operator of none-continuity and nonecompactness conditions is also...In this paper, the fixed point theorems of composite set-valued increasing operators are given. As a corollary, the fixed point theorem for increasing operator of none-continuity and nonecompactness conditions is also given. Some relevant results are improved and generalized.展开更多
Let E be a self-similar set satisfying the open set condition. Professor Xu conjectures in his doctoral degree thesis that if H^8（E） 〈｜E｜^8, then for any x ∈ E, the inequality ^-D^3C（E,x）〉H^8（E）/｜E｜^8hold...Let E be a self-similar set satisfying the open set condition. Professor Xu conjectures in his doctoral degree thesis that if H^8（E） 〈｜E｜^8, then for any x ∈ E, the inequality ^-D^3C（E,x）〉H^8（E）/｜E｜^8holds, where 3 = dimH（E）. The above conjecture is negatively answered in this＇paper.展开更多
In this paper, we discuss the existence of solution of a nonlinear two-point boundary value problem with a positive parameter Q arising in the study of surfacetension-induced flows of a liquid metal or semiconductor. ...In this paper, we discuss the existence of solution of a nonlinear two-point boundary value problem with a positive parameter Q arising in the study of surfacetension-induced flows of a liquid metal or semiconductor. By applying the Schauder's fixed-point theorem, we prove that the problem admits a solution for 0 ≤ Q ≤ 14.306.It improves the result of 0 ≤ Q ＜ 1 in [2] and 0 ≤ Q ≤ 13.213 in [3].展开更多
We study the following nonlinear m-point p-Laplacian boundary value problem with non-homogenous condition: (Φp(u′)′)+f(t, u, u′)=0, 0<t<1, u′(0)=0, u(1)-Σ m-2 i=1 kiu(ξi)=λ, where Φp(s)=|s|p-2 s, p>...We study the following nonlinear m-point p-Laplacian boundary value problem with non-homogenous condition: (Φp(u′)′)+f(t, u, u′)=0, 0<t<1, u′(0)=0, u(1)-Σ m-2 i=1 kiu(ξi)=λ, where Φp(s)=|s|p-2 s, p>1, λ>0, ki≥0(i = 1, 2, ··· , m-2), 0<ξ1<ξ2< ··· <ξm-2<1,0 < Σm-2 i=1 ki<1. Under sufficient conditions, we show that there exists a positive number λ* such that the problem has at least one positive solution for 0 < λ < λ and no solution for λ > λ*. The proof is based on the Schauder fixed point theorem and upper-lower technics.展开更多
The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solution...The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solutions. The proof is based on an application of Schauder’s fixed point theorem to a modified problem whose solutions are that of the original one. At the same time, Arzela Ascoli theorem is used to prove that the defined operator N is a compact map.展开更多
This paper is to investigate the positive solutions of the systems of second-order ordinary differential equations with nonhomogeneous multi-point boundary conditions. By the lower and upper solutions method, Schauder...This paper is to investigate the positive solutions of the systems of second-order ordinary differential equations with nonhomogeneous multi-point boundary conditions. By the lower and upper solutions method, Schauder fixed point theorem and fixed point index theory, under certain conditions, it is proved that there exist appropriate regions of parameters in which the problem has at least two, at least one or no positive solution.展开更多
文摘In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park （Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7（2000）, 1-28） to obtain an almost fixed point theorem for upper [resp., lower] semicontinuous multimaps in locally G-convex spaces, and then give a fixed point theorem for upper semicontinuous multimap with closed Γ-convex values.
基金partially supported by the foundation of the research item of Strong Department of Engineering Innovation, which is sponsored by the Strong School of Engineering Innovation of Hanshan Normal University, China, 2013partially supported by National Natural Science Foundation of China (No. 11371379)
文摘In this paper, some results on the upper convex densities of self-similar sets at the contracting-similarity fixed points are discussed. Firstly, a characterization of the upper convex densities of self-similar sets at the contracting-similarity fixed points is given. Next, under the strong separation open set condition, the existence of the best shape for the upper convex densities of self-similar sets at the contracting-similarity fixed points is proven. As consequences, an open problem and a conjecture, which were posed by Zhou and Xu, are answered.
文摘Based on the classical(matrix type)input-output analysis,a type of nonlinear (continuous type) conditional Leontief model,input-output equation were introduced,as well as three corresponding questions,namely,solvability,continuity and surjectivity,and some fixed point and surjectivity methods in nonlinear analysis were used to deal with these questions. As a result,the main theorems are obtained,which provide some sufficient criterions to solve above questions described by the boundary properties of the enterprises consuming operator.
文摘In this paper, using the context of complete partial metric spaces, some common fixed point results of maps that satisfy the generalized （ψ, Ф）-weak contractive conditions are obtained. Our results generalize, extend, unify, enrich and complement many existing results in the literature. Example are given showing the validaty of our results.
基金the National Natural Science Foundation of China
文摘The purpose of this paper is to obtain a generalization of the famous Browder's fixed point theorem and some equivalent forms. As application, these results are utilized to study the existence problems of fixed points and nearest points.
文摘We obtain some theorems for real increasing functions showing that elementary fixed point theory can bring to astonishing results by assuming only a few properties, some of which intrinsically possessed from these functions. An application is given for a theorem of quasi-compactness and a known result in posets is also recalled and applied to real intervals.
文摘In this work, we will discuss Caristi’s fixed point theorem for mapping results introduced in the setting of normed spaces. This work is a generalization of the classical Caristi’s fixed point theorem. Also, Caristi’s type of fixed points theorem was partial discussed in Reich, Mizoguchi and Takahashi’s and Amini-Harandi’s results, we developed ideas that many known fixed point theorems can easily be derived from the Caristi theorem.
文摘This paper aims at treating a study of Banach fixed point theorem for mapping results that introduced in the setting of normed space. The classical Banach fixed point theorem is a generalization of this work. A fixed point theory is a beautiful mixture of Mathematical analysis to explain some conditions in which maps give excellent solutions. Here later many mathematicians used this fixed point theory to establish their results, see for instance, Picard-Lindel of Theorem, The Picard theorem, Implicit function theorem etc. Also, we developed ideas that many of known fixed point theorems can easily be derived from the Banach theorem. It extends some recent works on the extension of Banach contraction principle to metric space with norm spaces.
基金Ministerio de Educacióny Ciencia and FEDER,Project MTM2004-06652-C03-01Xunta de Galicia and FEDER,Projects PGIDIT02PXIC20703PN and PGIDIT05PXIC20702PN
文摘We prove some fixed point theorems in partially ordered sets, providing an extension of the Banach contractive mapping theorem. Having studied previously the nondecreasing case, we consider in this paper nonincreasing mappings as well as non monotone mappings. We also present some applications to first-order ordinary differential equations with periodic boundary conditions, proving the existence of a unique solution admitting the existence of a lower solution.
文摘In this paper, the fixed point theorems of composite set-valued increasing operators are given. As a corollary, the fixed point theorem for increasing operator of none-continuity and nonecompactness conditions is also given. Some relevant results are improved and generalized.
文摘Let E be a self-similar set satisfying the open set condition. Professor Xu conjectures in his doctoral degree thesis that if H^8（E） 〈｜E｜^8, then for any x ∈ E, the inequality ^-D^3C（E,x）〉H^8（E）/｜E｜^8holds, where 3 = dimH（E）. The above conjecture is negatively answered in this＇paper.
基金The work was supported by National Natural Science Foundation(Grant No. 10471129) of China
文摘In this paper, we discuss the existence of solution of a nonlinear two-point boundary value problem with a positive parameter Q arising in the study of surfacetension-induced flows of a liquid metal or semiconductor. By applying the Schauder's fixed-point theorem, we prove that the problem admits a solution for 0 ≤ Q ≤ 14.306.It improves the result of 0 ≤ Q ＜ 1 in [2] and 0 ≤ Q ≤ 13.213 in [3].
文摘We study the following nonlinear m-point p-Laplacian boundary value problem with non-homogenous condition: (Φp(u′)′)+f(t, u, u′)=0, 0<t<1, u′(0)=0, u(1)-Σ m-2 i=1 kiu(ξi)=λ, where Φp(s)=|s|p-2 s, p>1, λ>0, ki≥0(i = 1, 2, ··· , m-2), 0<ξ1<ξ2< ··· <ξm-2<1,0 < Σm-2 i=1 ki<1. Under sufficient conditions, we show that there exists a positive number λ* such that the problem has at least one positive solution for 0 < λ < λ and no solution for λ > λ*. The proof is based on the Schauder fixed point theorem and upper-lower technics.
文摘The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solutions. The proof is based on an application of Schauder’s fixed point theorem to a modified problem whose solutions are that of the original one. At the same time, Arzela Ascoli theorem is used to prove that the defined operator N is a compact map.
文摘This paper is to investigate the positive solutions of the systems of second-order ordinary differential equations with nonhomogeneous multi-point boundary conditions. By the lower and upper solutions method, Schauder fixed point theorem and fixed point index theory, under certain conditions, it is proved that there exist appropriate regions of parameters in which the problem has at least two, at least one or no positive solution.
