The minimal-maximal fixed points theorems of increasing operators are proved in ordered space and some well-known results of increasing operators and monotone operators are improved and generalized. The obtained resul...The minimal-maximal fixed points theorems of increasing operators are proved in ordered space and some well-known results of increasing operators and monotone operators are improved and generalized. The obtained results are then applied to singular nonlinear boundary problem in ordinary differential equation without any assumption of continuity, compactness, convexity and concavity.展开更多
The Ti-axiom,the Ti-ordered axiom and Ti-pairwise axiom(i = 0,1,2,3,4) of topological ordered space are discussed and proved that they are equivalence under the certain conditions.
In this paper,we establish common fixed point theorems for expansive map?pings on b-metric-like space and coincidence point for f-weakly isotone increasing mappings in partially ordered b-metric-like space.The main re...In this paper,we establish common fixed point theorems for expansive map?pings on b-metric-like space and coincidence point for f-weakly isotone increasing mappings in partially ordered b-metric-like space.The main results generalize and extend several well-known comparable results from the existing literature.Moreover,some examples are provided to illustrate the main results.展开更多
In the paper quasi_weak convergence is introduced in ordered Banach space and it is weaker than weak convergence. Besed on it, the fixed point existence theorem of increasing operator is proved without the suppose of ...In the paper quasi_weak convergence is introduced in ordered Banach space and it is weaker than weak convergence. Besed on it, the fixed point existence theorem of increasing operator is proved without the suppose of continuity and compactness in the sense of norm and weak compactness and is applied to the Hammerstein nonlinear intergal equation.展开更多
Some common fixed point results for mappings satisfying a quasi-contractive condition which involves altering distance functions are obtained in partially ordered complete cone metric spaces. A sufficient condition fo...Some common fixed point results for mappings satisfying a quasi-contractive condition which involves altering distance functions are obtained in partially ordered complete cone metric spaces. A sufficient condition for the uniqueness of common fixed point is proved. Also, an example is given to support our results.展开更多
In this paper, a new concept of double coupled fixed point for multi-valued mixed increasing operators is given and some new double coupled fixed point theorems for multi-valued mixed increasing operators in ordered B...In this paper, a new concept of double coupled fixed point for multi-valued mixed increasing operators is given and some new double coupled fixed point theorems for multi-valued mixed increasing operators in ordered Banach spaces are also given. These results extend and generalize some results of Huang and Fang.展开更多
We provide convergence results and error estimates for Newton-like methods in generalized Banach spaces.The idea of a generalized norm is used whichis defined to be a map from a linear space into a partially ordered B...We provide convergence results and error estimates for Newton-like methods in generalized Banach spaces.The idea of a generalized norm is used whichis defined to be a map from a linear space into a partially ordered Banach space.Convergence results and error estimates are improved compared with the real norm theory.展开更多
In this paper, we introduce the concepts of g and b approximations via general ordered topological approximation spaces. Also, increasing (decreasing) g, b boundary, positive and negative regions are given in general ...In this paper, we introduce the concepts of g and b approximations via general ordered topological approximation spaces. Also, increasing (decreasing) g, b boundary, positive and negative regions are given in general ordered topological approximation spaces (GOTAS, for short). Some important properties of them were investigated. From this study, we can say that studying any properties of rough set concepts via GOTAS is a generalization of Pawlak approximation spaces and general approximation spaces.展开更多
In this paper, we establish the existence and uniqueness of fixed points of operator , when n is an arbitrary positive integer and X is a partially ordered complete metric space. We have shown examples to verify our w...In this paper, we establish the existence and uniqueness of fixed points of operator , when n is an arbitrary positive integer and X is a partially ordered complete metric space. We have shown examples to verify our work. Our results generalize the recent fixed point theorems cited in [1]-[4] etc. and include several recent developments.展开更多
In the paper [Monotone countable paracompactness and maps to ordered topological vector spaces, Top. Appl., 2014, 169（3）： 51–70], Yamazaki initiated the study on maps with values into ordered topological vector sp...In the paper [Monotone countable paracompactness and maps to ordered topological vector spaces, Top. Appl., 2014, 169（3）： 51–70], Yamazaki initiated the study on maps with values into ordered topological vector spaces. Characterizations of monotonically countably paracompact spaces and some other spaces in terms of maps to ordered topological vector spaces were obtained. In this paper, following Yamazaki＇s method, we present some characterizations of stratifiable spaces and k-semi-stratifiable spaces in terms of maps with values into ordered topological vector spaces.展开更多
The present work considers the endpoint in the abstract metric space. It firstly introduces the metric space of partially ordered groups and the metric space of partially ordered modules, respectively;and defines the ...The present work considers the endpoint in the abstract metric space. It firstly introduces the metric space of partially ordered groups and the metric space of partially ordered modules, respectively;and defines the convergence of sequences and the multi-valued weak contractions, etc., on the introduced space. And then, with the methods of functional analysis and abstract algebra, it successively establishes an endpoint theorem for the metric space of partially ordered groups and an endpoint theorem for the metric space of partially ordered modules. The contributions of this article extend the theory of cone metric space constructed by Huang and Zhang (2007) and some recent results on the fixed point and endpoint theory, such as the endpoint theorem given by Amini-Harandi (2010).展开更多
In this paper, some characterizations of pairwise semi-stratifiable spaces are given by means of pairwise g-functions and semi-continuous functions and the pairwise semi-stratifiability of topological ordered C-spaces...In this paper, some characterizations of pairwise semi-stratifiable spaces are given by means of pairwise g-functions and semi-continuous functions and the pairwise semi-stratifiability of topological ordered C-spaces with semi-stratifiable topology is discussed.展开更多
Recently, many new features of Sobolev spaces W k,p ？RN ？ were studied in [4-6, 32]. This paper is devoted to giving a brief review of some known characterizations of Sobolev spaces in Euclidean spaces and describin...Recently, many new features of Sobolev spaces W k,p ？RN ？ were studied in [4-6, 32]. This paper is devoted to giving a brief review of some known characterizations of Sobolev spaces in Euclidean spaces and describing our recent study of new characterizations of Sobolev spaces on both Heisenberg groups and Euclidean spaces obtained in [12] and [13] and outlining their proofs. Our results extend those characterizations of first order Sobolev spaces in [32] to the Heisenberg group setting. Moreover, our theorems also provide diff erent characterizations for the second order Sobolev spaces in Euclidean spaces from those in [4, 5].展开更多
Kizmaz [13] studied the difference sequence spaces ∞（A）, c（A）, and co（A）. Several article dealt with the sets of sequences of m-th order difference of which are bounded, convergent, or convergent to zero. Alta...Kizmaz [13] studied the difference sequence spaces ∞（A）, c（A）, and co（A）. Several article dealt with the sets of sequences of m-th order difference of which are bounded, convergent, or convergent to zero. Altay and Basar [5] and Altay, Basar, and Mursaleen [7] introduced the Euler sequence spaces e0^r, ec^r, and e∞^r, respectively. The main purpose of this article is to introduce the spaces e0^r△^（m））, ec^r△^（m））, and e∞^r△^（m））consisting of all sequences whose mth order differences are in the Euler spaces e0^r, ec^r, and e∞^r, respectively. Moreover, the authors give some topological properties and inclusion relations, and determine the α-, β-, and γ-duals of the spaces e0^r△^（m））, ec^r△^（m））, and e∞^r△^（m））, and the Schauder basis of the spaces e0^r△^（m））, ec^r△^（m））. The last section of the article is devoted to the characterization of some matrix mappings on the sequence space ec^r△^（m））.展开更多
In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Basar （[17]） defined the Euler spaces of m-th order difference sequences e r 0 （△ （ m ） ）, e r c （△ （...In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Basar （[17]） defined the Euler spaces of m-th order difference sequences e r 0 （△ （ m ） ）, e r c （△ （ m ） ） and e r ∞ （△ （ m ） ） and characterized some classes of matrix transformations on them. In our paper, we add a new supplementary aspect to their research by characterizing classes of compact operators on those spaces. For that purpose, the spaces are treated as the matrix domains of a triangle in the classical sequence spaces c 0 , c and ∞ . The main tool for our characterizations is the Hausdorff measure of noncompactness.展开更多
This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a c...This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.展开更多
The Besov spaces B_p^(α,4)(Γ)and Triebel-Lizorkin spaces F_p^(α,4)(Γ)with high order x∈R on a Lipschitz curve Γ are defind,when 1≤p≤∞,1≤q≤∞.To compare to the classical case.a difference characterization of...The Besov spaces B_p^(α,4)(Γ)and Triebel-Lizorkin spaces F_p^(α,4)(Γ)with high order x∈R on a Lipschitz curve Γ are defind,when 1≤p≤∞,1≤q≤∞.To compare to the classical case.a difference characterization of such spaces in the case|x|<1 is given also.展开更多
In this paper, the initial value problems of second order ordinary differential equations in Banach spaces are discussed. By using the monotone iterative technique, some existence and uniqueness theorems for solutions...In this paper, the initial value problems of second order ordinary differential equations in Banach spaces are discussed. By using the monotone iterative technique, some existence and uniqueness theorems for solutions are obtained.展开更多
We show for the Benjamin-Ono equation an existence uniqeness theorem in Sobolev spaces of arbitrary fractional order s greater-than-or-equal-to 2, provided the initial data is given in the same space.
It is important to study the propagation and interaction of progressing waves of nonlinear equations in the class of piecewise smooth function. However, there has not been many works on that in multidimensional case. ...It is important to study the propagation and interaction of progressing waves of nonlinear equations in the class of piecewise smooth function. However, there has not been many works on that in multidimensional case. In 1985, J, Rauch & M. Reed have provad the existence and uniqueness of piecewise smooth solution for展开更多
文摘The minimal-maximal fixed points theorems of increasing operators are proved in ordered space and some well-known results of increasing operators and monotone operators are improved and generalized. The obtained results are then applied to singular nonlinear boundary problem in ordinary differential equation without any assumption of continuity, compactness, convexity and concavity.
基金The project is supported by the NNSF of China(No.10971185,10971186)Fujian Province support college research plan project(No.JK2011031)
文摘The Ti-axiom,the Ti-ordered axiom and Ti-pairwise axiom(i = 0,1,2,3,4) of topological ordered space are discussed and proved that they are equivalence under the certain conditions.
基金Supported by the National Natural Science Foundation of China(12001249)the Natural Science Foundation of Jiangxi Province(20232BAB211004)the Educational Commission Science Programm of Jiangxi Province(GJJ2200523)。
文摘In this paper,we establish common fixed point theorems for expansive map?pings on b-metric-like space and coincidence point for f-weakly isotone increasing mappings in partially ordered b-metric-like space.The main results generalize and extend several well-known comparable results from the existing literature.Moreover,some examples are provided to illustrate the main results.
文摘In the paper quasi_weak convergence is introduced in ordered Banach space and it is weaker than weak convergence. Besed on it, the fixed point existence theorem of increasing operator is proved without the suppose of continuity and compactness in the sense of norm and weak compactness and is applied to the Hammerstein nonlinear intergal equation.
基金Supported by the National Natural Science Foundation of China（11271293）
文摘Some common fixed point results for mappings satisfying a quasi-contractive condition which involves altering distance functions are obtained in partially ordered complete cone metric spaces. A sufficient condition for the uniqueness of common fixed point is proved. Also, an example is given to support our results.
基金Funded by the Natural Science Foundation of China (No. 10171070)
文摘In this paper, a new concept of double coupled fixed point for multi-valued mixed increasing operators is given and some new double coupled fixed point theorems for multi-valued mixed increasing operators in ordered Banach spaces are also given. These results extend and generalize some results of Huang and Fang.
文摘We provide convergence results and error estimates for Newton-like methods in generalized Banach spaces.The idea of a generalized norm is used whichis defined to be a map from a linear space into a partially ordered Banach space.Convergence results and error estimates are improved compared with the real norm theory.
文摘In this paper, we introduce the concepts of g and b approximations via general ordered topological approximation spaces. Also, increasing (decreasing) g, b boundary, positive and negative regions are given in general ordered topological approximation spaces (GOTAS, for short). Some important properties of them were investigated. From this study, we can say that studying any properties of rough set concepts via GOTAS is a generalization of Pawlak approximation spaces and general approximation spaces.
文摘In this paper, we establish the existence and uniqueness of fixed points of operator , when n is an arbitrary positive integer and X is a partially ordered complete metric space. We have shown examples to verify our work. Our results generalize the recent fixed point theorems cited in [1]-[4] etc. and include several recent developments.
基金Supported by the National Natural Science Foundation of China(Grant No.11401262)
文摘In the paper [Monotone countable paracompactness and maps to ordered topological vector spaces, Top. Appl., 2014, 169（3）： 51–70], Yamazaki initiated the study on maps with values into ordered topological vector spaces. Characterizations of monotonically countably paracompact spaces and some other spaces in terms of maps to ordered topological vector spaces were obtained. In this paper, following Yamazaki＇s method, we present some characterizations of stratifiable spaces and k-semi-stratifiable spaces in terms of maps with values into ordered topological vector spaces.
文摘The present work considers the endpoint in the abstract metric space. It firstly introduces the metric space of partially ordered groups and the metric space of partially ordered modules, respectively;and defines the convergence of sequences and the multi-valued weak contractions, etc., on the introduced space. And then, with the methods of functional analysis and abstract algebra, it successively establishes an endpoint theorem for the metric space of partially ordered groups and an endpoint theorem for the metric space of partially ordered modules. The contributions of this article extend the theory of cone metric space constructed by Huang and Zhang (2007) and some recent results on the fixed point and endpoint theory, such as the endpoint theorem given by Amini-Harandi (2010).
基金Supported by the National Natural Science Foundation of China(Grant Nos.1097118510971186+3 种基金11201414)Fujian Province Support College Research Plan Project(Grant No.JK2011031)the Natural Science Foundation of Fujian Province(Grant Nos.2012J050132013J01029)
文摘In this paper, some characterizations of pairwise semi-stratifiable spaces are given by means of pairwise g-functions and semi-continuous functions and the pairwise semi-stratifiability of topological ordered C-spaces with semi-stratifiable topology is discussed.
文摘Recently, many new features of Sobolev spaces W k,p ？RN ？ were studied in [4-6, 32]. This paper is devoted to giving a brief review of some known characterizations of Sobolev spaces in Euclidean spaces and describing our recent study of new characterizations of Sobolev spaces on both Heisenberg groups and Euclidean spaces obtained in [12] and [13] and outlining their proofs. Our results extend those characterizations of first order Sobolev spaces in [32] to the Heisenberg group setting. Moreover, our theorems also provide diff erent characterizations for the second order Sobolev spaces in Euclidean spaces from those in [4, 5].
文摘Kizmaz [13] studied the difference sequence spaces ∞（A）, c（A）, and co（A）. Several article dealt with the sets of sequences of m-th order difference of which are bounded, convergent, or convergent to zero. Altay and Basar [5] and Altay, Basar, and Mursaleen [7] introduced the Euler sequence spaces e0^r, ec^r, and e∞^r, respectively. The main purpose of this article is to introduce the spaces e0^r△^（m））, ec^r△^（m））, and e∞^r△^（m））consisting of all sequences whose mth order differences are in the Euler spaces e0^r, ec^r, and e∞^r, respectively. Moreover, the authors give some topological properties and inclusion relations, and determine the α-, β-, and γ-duals of the spaces e0^r△^（m））, ec^r△^（m））, and e∞^r△^（m））, and the Schauder basis of the spaces e0^r△^（m））, ec^r△^（m））. The last section of the article is devoted to the characterization of some matrix mappings on the sequence space ec^r△^（m））.
基金supported by the research project#144003 of the Serbian Ministry of Science, Technology and Development
文摘In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Basar （[17]） defined the Euler spaces of m-th order difference sequences e r 0 （△ （ m ） ）, e r c （△ （ m ） ） and e r ∞ （△ （ m ） ） and characterized some classes of matrix transformations on them. In our paper, we add a new supplementary aspect to their research by characterizing classes of compact operators on those spaces. For that purpose, the spaces are treated as the matrix domains of a triangle in the classical sequence spaces c 0 , c and ∞ . The main tool for our characterizations is the Hausdorff measure of noncompactness.
文摘This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.
基金The author is supported in part by the Foundation of Zhongshan University Advanced Research Centre and NSF of China.
文摘The Besov spaces B_p^(α,4)(Γ)and Triebel-Lizorkin spaces F_p^(α,4)(Γ)with high order x∈R on a Lipschitz curve Γ are defind,when 1≤p≤∞,1≤q≤∞.To compare to the classical case.a difference characterization of such spaces in the case|x|<1 is given also.
文摘In this paper, the initial value problems of second order ordinary differential equations in Banach spaces are discussed. By using the monotone iterative technique, some existence and uniqueness theorems for solutions are obtained.
文摘We show for the Benjamin-Ono equation an existence uniqeness theorem in Sobolev spaces of arbitrary fractional order s greater-than-or-equal-to 2, provided the initial data is given in the same space.
基金This paper is supported by the National Foundations.
文摘It is important to study the propagation and interaction of progressing waves of nonlinear equations in the class of piecewise smooth function. However, there has not been many works on that in multidimensional case. In 1985, J, Rauch & M. Reed have provad the existence and uniqueness of piecewise smooth solution for
