In complete metric spaces, the common fixed point theorems for sequences of φ-type contraction set-valued mappings are established, and the corresponding random com- mon fixed point theorems for set-valued mappings a...In complete metric spaces, the common fixed point theorems for sequences of φ-type contraction set-valued mappings are established, and the corresponding random com- mon fixed point theorems for set-valued mappings are also obtained.展开更多
Under the conditions of compatility or sub -c ompatility between a sigle-valued mapping and set-valued mapping, this paper d iscusses the existence of common fixed points for two set-valued mappings and a single-value...Under the conditions of compatility or sub -c ompatility between a sigle-valued mapping and set-valued mapping, this paper d iscusses the existence of common fixed points for two set-valued mappings and a single-valued mapping in complete, convex matric spaces. We extend and develop the main results.展开更多
Fixed points for set_valued mappings from a metric space X (not necessarily complete) into B(X), the collection of nonempty bounded subsets of X are obtained. The result generalizes some known results.
In this paper, we give a survey on the PhD thesis of the first author. There theexistence and ergodicity on invariant measures of set-valued mappings are discused.
SINCE 1956, Michael’s continuous selection theory has been applied to functional analysis,topology, approximation theory and other mathematical fields. In this letter, the concept ofthe pseudo-lower semicontinuity is...SINCE 1956, Michael’s continuous selection theory has been applied to functional analysis,topology, approximation theory and other mathematical fields. In this letter, the concept ofthe pseudo-lower semicontinuity is introduced, and a convex structure of metric space is de-fined. A continuous selection theorem for pseudo-lower semicontinuity is given. This展开更多
Consider the continuous map f:x→X and the continuous map f of K,(X)into itself induced by f,where X is a metric space and K(X)the space of all non-empty compact subsets of x endowed with the Hausdorff metric.Accordin...Consider the continuous map f:x→X and the continuous map f of K,(X)into itself induced by f,where X is a metric space and K(X)the space of all non-empty compact subsets of x endowed with the Hausdorff metric.According to the questions whether the chaoticity of f implies the chaoticity of f posed by Roman-Flores and when the chaoticity of f implies the chaoticity of f posed by Fedeli,we investigate the relations between f and f in the related dynamical properties such as transitivity,weakly mixing and mixing,etc.And by using the obtained results,we give the satisfied answers to Roman-Flores's question and Fedeli's question.展开更多
In this paper, we derive a general vector Ekeland variational principle for set-valued mappings, which has a dosed relation to εk^0 -efficient points of set-valued optimization problems. The main result presented in ...In this paper, we derive a general vector Ekeland variational principle for set-valued mappings, which has a dosed relation to εk^0 -efficient points of set-valued optimization problems. The main result presented in this paper is a generalization of the corresponding result in [3].展开更多
A new coincidence theorem for admissible set-valued mappings is proved in FC-spaces with a more general convexity structure. As applications, an abstract variational inequality, a KKM type theorem and a fixed point th...A new coincidence theorem for admissible set-valued mappings is proved in FC-spaces with a more general convexity structure. As applications, an abstract variational inequality, a KKM type theorem and a fixed point theorem are obtained. Our results generalize and improve the corresponding results in the literature.展开更多
We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approx...We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108.展开更多
In this paper,we discuss the continuities of some natural mappings on pointcompact continuous set-valued mapping spaces with compact-open topology and obtain the properties of set-valued injective mappings,set-valued ...In this paper,we discuss the continuities of some natural mappings on pointcompact continuous set-valued mapping spaces with compact-open topology and obtain the properties of set-valued injective mappings,set-valued diagonal mappings,induced mappings,set-valued evaluation mappings,set-valued topological sum mappings and set-valued topological product mappings.展开更多
Under new assumptions,this paper obtains some extended versions of Ky Fan type inequality for a family of C-continuous set-valued mappings in the setting of topological semilattices.The obtained results are new and di...Under new assumptions,this paper obtains some extended versions of Ky Fan type inequality for a family of C-continuous set-valued mappings in the setting of topological semilattices.The obtained results are new and different from the corresponding known results in the literature.Some special cases of the main result are also discussed.Some examples are given to illustrate the results.展开更多
冶金尘泥的转底炉处理工艺是目前钢铁行业采用的主要处置工艺,但在实际生产过程中经常出现还原焙烧不均匀的问题。利用微观扫描电子显微镜(scanning electron microscopy,SEM)分析结合宏观Maps统计分析,对冶金尘泥还原焙烧的不均匀性进...冶金尘泥的转底炉处理工艺是目前钢铁行业采用的主要处置工艺,但在实际生产过程中经常出现还原焙烧不均匀的问题。利用微观扫描电子显微镜(scanning electron microscopy,SEM)分析结合宏观Maps统计分析,对冶金尘泥还原焙烧的不均匀性进行详细的可视化、数据化分析。研究结果表明,冶金尘泥在焙烧温度为1250℃、焙烧时间为15 min的条件下,熟球金属化率达到89.04%、脱锌率达到81.66%、抗压强度达到3.03 kN,熟球金属化率和脱锌率会随着焙烧温度提高和焙烧时间延长而进一步提高,但熟球抗压强度在焙烧时间过长时反而逐渐降低;熟球Maps统计分析表明,提高焙烧温度更有利于提高熟球外圈和下部的还原程度,而延长焙烧时间也更有利于提高熟球下部还原程度,但对熟球内部和外圈还原程度的提升作用比较相似;同时,提高焙烧温度也更有利于提升熟球下部的致密化程度,降低熟球上、下孔隙结构的不均匀性,进而显著提高熟球整体抗压强度;但焙烧时间过长会导致熟球中小孔隙融合为大孔隙,反而降低熟球抗压强度。此外,熟球中硅酸盐(渣相)和浮氏体(FexO)更容易破裂,而金属铁(Fe)可延缓裂纹蔓延,因而,适当提高熟球金属化率、降低硅酸盐(渣相)含量也有利于提高其抗压强度。基于Maps统计分析探究了冶金尘泥还原焙烧过程中物相及孔隙的变化规律,分析结果可以为转底炉工艺处理冶金尘泥的生产实践提供指导和建议。展开更多
A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condit...A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established, its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the set-valued map is specialized to be a single-valued map.展开更多
Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. U...Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. Under the assumption of generalized subconvexlikeness, scalarization, multiplier and saddle point theorems are obtained in the sense of Benson proper efficiency.展开更多
In this paper,the ε-super effcient solution for set-valued map vector optimization in locally convex space is introduced.And under the assumption of the nearly generalized cone-subconvexlikeness for set-valued maps,u...In this paper,the ε-super effcient solution for set-valued map vector optimization in locally convex space is introduced.And under the assumption of the nearly generalized cone-subconvexlikeness for set-valued maps,used new methods,the scalarization theorem and Lagrange multiplier theorem for ε-super effcient solution are established.展开更多
In this paper, we consider the following subadditive set-valued map F ： X→P0（Y） ：where r and s are two natural numbers. And we discuss the existence and unique problem of additive selection maps for the above set...In this paper, we consider the following subadditive set-valued map F ： X→P0（Y） ：where r and s are two natural numbers. And we discuss the existence and unique problem of additive selection maps for the above set-valued map.展开更多
基金Foundation item： Supported by the Science Foundation from the Ministry of Education of Jiangsu Province（04KJD110168, 06KJBll0107）
文摘In complete metric spaces, the common fixed point theorems for sequences of φ-type contraction set-valued mappings are established, and the corresponding random com- mon fixed point theorems for set-valued mappings are also obtained.
文摘Under the conditions of compatility or sub -c ompatility between a sigle-valued mapping and set-valued mapping, this paper d iscusses the existence of common fixed points for two set-valued mappings and a single-valued mapping in complete, convex matric spaces. We extend and develop the main results.
文摘Fixed points for set_valued mappings from a metric space X (not necessarily complete) into B(X), the collection of nonempty bounded subsets of X are obtained. The result generalizes some known results.
文摘In this paper, we give a survey on the PhD thesis of the first author. There theexistence and ergodicity on invariant measures of set-valued mappings are discused.
文摘SINCE 1956, Michael’s continuous selection theory has been applied to functional analysis,topology, approximation theory and other mathematical fields. In this letter, the concept ofthe pseudo-lower semicontinuity is introduced, and a convex structure of metric space is de-fined. A continuous selection theorem for pseudo-lower semicontinuity is given. This
基金supported by the National Natural Science Foundation of China(Grant No.19971035)the Innovation Foundation of Jilin University(Grant No.2004CZ051).
文摘Consider the continuous map f:x→X and the continuous map f of K,(X)into itself induced by f,where X is a metric space and K(X)the space of all non-empty compact subsets of x endowed with the Hausdorff metric.According to the questions whether the chaoticity of f implies the chaoticity of f posed by Roman-Flores and when the chaoticity of f implies the chaoticity of f posed by Fedeli,we investigate the relations between f and f in the related dynamical properties such as transitivity,weakly mixing and mixing,etc.And by using the obtained results,we give the satisfied answers to Roman-Flores's question and Fedeli's question.
基金Supported by the National Natural Science Foundation of China(No.60574073,No.10471142)
文摘In this paper, we derive a general vector Ekeland variational principle for set-valued mappings, which has a dosed relation to εk^0 -efficient points of set-valued optimization problems. The main result presented in this paper is a generalization of the corresponding result in [3].
基金Supported by the National Natural Science Foundation of China (No. 10771173)the Natural Science Foundation of Henan Education Department (No. 2008B110012)+1 种基金the Science and Technology Program Project of Henan Province (No. 092300410187)the Youth Foundation of Luoyang Normal University
文摘A new coincidence theorem for admissible set-valued mappings is proved in FC-spaces with a more general convexity structure. As applications, an abstract variational inequality, a KKM type theorem and a fixed point theorem are obtained. Our results generalize and improve the corresponding results in the literature.
基金the Natural Science Foundation of China (No. 10471151)the Educational Science Foundation of Chongqing (KJ051307).
文摘We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108.
基金Supported by the Science Foundation of Hangzhou Normal University（02010180）
文摘In this paper,we discuss the continuities of some natural mappings on pointcompact continuous set-valued mapping spaces with compact-open topology and obtain the properties of set-valued injective mappings,set-valued diagonal mappings,induced mappings,set-valued evaluation mappings,set-valued topological sum mappings and set-valued topological product mappings.
基金partially supported by NAFOSTED under Grant No.101.01-2014.17UTC under Grant No.T2017-KHCB-60
文摘Under new assumptions,this paper obtains some extended versions of Ky Fan type inequality for a family of C-continuous set-valued mappings in the setting of topological semilattices.The obtained results are new and different from the corresponding known results in the literature.Some special cases of the main result are also discussed.Some examples are given to illustrate the results.
文摘冶金尘泥的转底炉处理工艺是目前钢铁行业采用的主要处置工艺,但在实际生产过程中经常出现还原焙烧不均匀的问题。利用微观扫描电子显微镜(scanning electron microscopy,SEM)分析结合宏观Maps统计分析,对冶金尘泥还原焙烧的不均匀性进行详细的可视化、数据化分析。研究结果表明,冶金尘泥在焙烧温度为1250℃、焙烧时间为15 min的条件下,熟球金属化率达到89.04%、脱锌率达到81.66%、抗压强度达到3.03 kN,熟球金属化率和脱锌率会随着焙烧温度提高和焙烧时间延长而进一步提高,但熟球抗压强度在焙烧时间过长时反而逐渐降低;熟球Maps统计分析表明,提高焙烧温度更有利于提高熟球外圈和下部的还原程度,而延长焙烧时间也更有利于提高熟球下部还原程度,但对熟球内部和外圈还原程度的提升作用比较相似;同时,提高焙烧温度也更有利于提升熟球下部的致密化程度,降低熟球上、下孔隙结构的不均匀性,进而显著提高熟球整体抗压强度;但焙烧时间过长会导致熟球中小孔隙融合为大孔隙,反而降低熟球抗压强度。此外,熟球中硅酸盐(渣相)和浮氏体(FexO)更容易破裂,而金属铁(Fe)可延缓裂纹蔓延,因而,适当提高熟球金属化率、降低硅酸盐(渣相)含量也有利于提高其抗压强度。基于Maps统计分析探究了冶金尘泥还原焙烧过程中物相及孔隙的变化规律,分析结果可以为转底炉工艺处理冶金尘泥的生产实践提供指导和建议。
文摘A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established, its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the set-valued map is specialized to be a single-valued map.
文摘Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. Under the assumption of generalized subconvexlikeness, scalarization, multiplier and saddle point theorems are obtained in the sense of Benson proper efficiency.
基金Supported by the Natural Science Foundation of the Education Department of Henan Province（2004110008）
文摘In this paper,the ε-super effcient solution for set-valued map vector optimization in locally convex space is introduced.And under the assumption of the nearly generalized cone-subconvexlikeness for set-valued maps,used new methods,the scalarization theorem and Lagrange multiplier theorem for ε-super effcient solution are established.
基金Supported by Science Foundation of Education Committee of Jilin Province of China([2011]No.434)
文摘In this paper, we consider the following subadditive set-valued map F ： X→P0（Y） ：where r and s are two natural numbers. And we discuss the existence and unique problem of additive selection maps for the above set-valued map.
