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Ostrowski’s Type Inequalities for Generalized(h,m)−Preinvex Functions with Its Applications
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作者 LI Ran LIAN Tie-yan 《Chinese Quarterly Journal of Mathematics》 2024年第3期270-287,共18页
A new concept generalized(h,m)−preinvex function on Yang’s fractal sets is proposed.Some Ostrowski’s type inequalities with two parameters for generalized(h,m)−preinvex function are established,where three local fra... A new concept generalized(h,m)−preinvex function on Yang’s fractal sets is proposed.Some Ostrowski’s type inequalities with two parameters for generalized(h,m)−preinvex function are established,where three local fractional inequalities involving generalized midpoint type,trapezoid type and Simpson type are derived as consequences.Furthermore,as some applications,special means inequalities and numerical quadratures for local fractional integrals are discussed. 展开更多
关键词 Generalized(h m)−preinvex function Hermite−Hadamard inequality Ostrowski inequality Simpson inequality
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KUHN-TUCKER CONDITION AND WOLFE DUALITY OF PREINVEX SET-VALUED OPTIMIZATION 被引量:2
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作者 盛宝怀 刘三阳 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第12期1655-1664,共10页
The optimality Kuhn-Tucker condition and the wolfe duality for the preinvex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order S-preinvex set-valued function... The optimality Kuhn-Tucker condition and the wolfe duality for the preinvex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order S-preinvex set-valued function were introduced, from which the properties of the corresponding contingent cone and the alpha-order contingent derivative were studied. Finally, the optimality Kuhn-Tucker condition and the Wolfe duality theorem for the alpha-order S-preinvex set-valued optimization were presented with the help of the alpha-order contingent derivative. 展开更多
关键词 preinvex set-valued function contingent epiderivatives optimality conditions DUALITY
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CONE-DIRECTED CONTINGENT DERIVATIVES AND GENERALIZED PREINVEX SET-VALUED OPTIMIZATION 被引量:10
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作者 丘京辉 《Acta Mathematica Scientia》 SCIE CSCD 2007年第1期211-218,共8页
By using cone-directed contingent derivatives, the unified necessary and sufficient optimality conditions are given for weakly and strongly minimal elements respectively in generalized preinvex set-valued optimization.
关键词 preinvex set-valued optimization cone-directed contingent derivative optimality conditions
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Monotone Set-Valued Function Defined by Set-Valued Choquet Integral
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作者 孙红霞 张强 《Journal of Beijing Institute of Technology》 EI CAS 2010年第2期241-245,共5页
Structural characteristics and absolute continuities of monotone set-valued function defined by set- valued Choquet integral are discussed. Similar to the single-valued monotone set function, several important structu... Structural characteristics and absolute continuities of monotone set-valued function defined by set- valued Choquet integral are discussed. Similar to the single-valued monotone set function, several important structural characteristics of set-valued function are defined and have been proven the same as those in the original set functions, such as null-additivity, weakly null-additivity, order continuity, strong order continuity and property(S). A counterexample shows that order continuity and strong order continuity of the original set functions are no longer kept in a monotone set-valued function when Choquet integrably bounded assumption is abandoned. Four kinds of absolute continuities are defined for set-valued function, and all been proven valid with respect to the original set functions. 展开更多
关键词 monotone set-valued function set-valued Choquet integral Choquet integral
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Gap Functions and Error Bounds for Set-Valued Vector Quasi Variational Inequality Problems
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作者 Rachana Gupta Aparna Mehra 《Applied Mathematics》 2017年第12期1903-1917,共15页
One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deri... One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deriving the error bounds which provide an estimated distance between a specific point and the exact solution of variational inequality problem. In this paper, we follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter. The error bounds results are obtained under fixed point symmetric and locally α-Holder assumptions on the set-valued map describing the domain of solution space of a set-valued vector quasi variational inequality problem. 展开更多
关键词 set-valued VECTOR QUASI Variational Inequality Problem GAP function Regularized GAP function Error Bounds Fixed Point Symmetric MAP α-Holder MAP
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Uniformly Bounded Set-Valued Composition Operators in the Spaces of Functions of Bounded Variation in the Sense of Riesz
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作者 Wadie Aziz Nelson Merentes 《International Journal of Modern Nonlinear Theory and Application》 2015年第4期226-233,共8页
We show that the lateral regularizations of the generator of any uniformly bounded set-valued composition Nemytskij operator acting in the spaces of functions of bounded variation in the sense of Riesz, with nonempty ... We show that the lateral regularizations of the generator of any uniformly bounded set-valued composition Nemytskij operator acting in the spaces of functions of bounded variation in the sense of Riesz, with nonempty bounded closed and convex values, are an affine function. 展开更多
关键词 j-Variation in the SENSE of RIESZ set-valued functions Left and Right Regularizations UNIFORMLY BOUNDED OPERATOR Composition (Nemytskij) OPERATOR Jensen Equation
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Optimality for Henig Proper Efficiency in Vector Optimization Involving Dini Set-Valued Directional Derivatives
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作者 Guolin Yu Huaipeng Bai 《Applied Mathematics》 2011年第7期922-925,共4页
This note studies the optimality conditions of vector optimization problems involving generalized convexity in locally convex spaces. Based upon the concept of Dini set-valued directional derivatives, the necessary an... This note studies the optimality conditions of vector optimization problems involving generalized convexity in locally convex spaces. Based upon the concept of Dini set-valued directional derivatives, the necessary and sufficient optimality conditions are established for Henig proper and strong minimal solutions respectively in generalized preinvex vector optimization problems. 展开更多
关键词 VECTOR Optimization Dini set-valued Directional DERIVATIVE Generalized preinvex function Henig PROPER Efficiency
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Hermite-Hadamard Type Inequalities for Operator h-preinvex Functions
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作者 Lian Tie-yan Tang Wei Ji You-qing 《Communications in Mathematical Research》 CSCD 2019年第2期180-192,共13页
Operator h-preinvex functions are introduced and a refinement of HermiteHadamard type inequalities for such functions is established. Results proved in this paper are more general and some known results are special ca... Operator h-preinvex functions are introduced and a refinement of HermiteHadamard type inequalities for such functions is established. Results proved in this paper are more general and some known results are special cases. 展开更多
关键词 Hermite-Hadamard's integral INEQUALITY OPERATOR h-preinvex function OPERATOR beta-preinvex function
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A survey of ergodicity on the set-valued mappings
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作者 ZHANGYu-cheng LIAOGong-fu 《海南师范学院学报(自然科学版)》 2004年第4期305-311,共7页
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.
关键词 set-valued mapping INVARIANT measure ERGODIC MARKOV operator Mark-ov transition function lower SEMICONTINUOUS continuous selection
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预不变凸函数的q-Hermite-Hadamard型不等式和广义的q-Iyengar型不等式
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作者 时统业 曾志红 曹俊飞 《汕头大学学报(自然科学版)》 2024年第4期24-32,共9页
研究量子积分的Hermite-Hadamard型不等式和Iyengar型不等式,首先建立带有一个参数的量子积分恒等式,然后用引入参数求最值的方法,建立了量子积分的广义的Iyengar型不等式;在一阶量子导数的绝对值是预不变凸函数的情形下,建立了量子积分... 研究量子积分的Hermite-Hadamard型不等式和Iyengar型不等式,首先建立带有一个参数的量子积分恒等式,然后用引入参数求最值的方法,建立了量子积分的广义的Iyengar型不等式;在一阶量子导数的绝对值是预不变凸函数的情形下,建立了量子积分的Hermite-Hadamard型不等式. 展开更多
关键词 Iyengar型不等式 Hermite-Hadamard型不等式 量子积分 预不变凸函数
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关于Semistrict Preinvex函数的几个性质
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作者 李成进 张圣贵 《福建师范大学学报(自然科学版)》 CAS CSCD 北大核心 2005年第2期14-17,共4页
给出了semistrictpreinvex函数与invex函数之间的关系以及semistrictpreinvex函数与strictprein vex函数之间的关系.
关键词 INVEX函数 semistrict preinvex函数 STRICT preinvex函数
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G-E-preinvex函数的几个性质
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作者 段誉 孙歆 陈兆阳 《毕节学院学报(综合版)》 2010年第8期39-42,共4页
给出G-E-preinvex函数的定义,并讨论了此函数的若干性质,其结论推广了相关文献中的结论。
关键词 G-E—preinvex函数 E-不变凸集 G-E-prequasiinvex函数
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多元α-预不变凸函数的Hermite-Hadamard型积分不等式 被引量:1
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作者 王海英 符祖峰 +1 位作者 李婧 谭冰 《湖北民族大学学报(自然科学版)》 CAS 2023年第2期246-251,共6页
论文研究了α-预不变凸函数的Hermite-Hadamard型积分不等式。利用Holder不等式、幂平均不等式和函数的α-预不变凸性,对此类广义凸函数的Hermite-Hadamard型积分不等式的左右两边分别给出估计值。借助多元α-预不变凸函数与单变量凸函... 论文研究了α-预不变凸函数的Hermite-Hadamard型积分不等式。利用Holder不等式、幂平均不等式和函数的α-预不变凸性,对此类广义凸函数的Hermite-Hadamard型积分不等式的左右两边分别给出估计值。借助多元α-预不变凸函数与单变量凸函数之间的关系,将此类函数的Hermite-Hadamard型不等式结果进行推广,得到了多元α-预不变凸函数的2个Hermite-Hadamard型积分不等式。 展开更多
关键词 α-预不变凸函数 Hermite-Hadamard型积分不等式 HOLDER不等式 幂平均不等式 单变量凸函数
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E-预不变凸函数的Hermite-Hadamard型积分不等式及应用
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作者 王海英 符祖峰 +1 位作者 高景利 虎大力 《南阳师范学院学报》 CAS 2023年第6期22-28,共7页
建立了E-预不变凸函数的Hermite-Hadamard型积分不等式。首先,利用分部积分法和变量代换,建立了E-预不变凸函数的Hermite-Hadamard型积分不等式。其次,利用Holder不等式、幂平均不等式和函数的E-预不变凸性,对获得的此类广义凸函数的Her... 建立了E-预不变凸函数的Hermite-Hadamard型积分不等式。首先,利用分部积分法和变量代换,建立了E-预不变凸函数的Hermite-Hadamard型积分不等式。其次,利用Holder不等式、幂平均不等式和函数的E-预不变凸性,对获得的此类广义凸函数的Hermite-Hadamard型积分不等式的左右两边的不等式分别给出估计值。接着,利用多元E-预不变凸函数与单变量凸函数之间的关系,将建立的Hermite-Hadamard型不等式结果进行推广,得到了多元E-预不变凸函数的两个Hermite-Hadamard型积分不等式。最后,给出了E-预不变凸函数的Hermite-Hadamard型积分不等式在一些特殊均值上的应用。 展开更多
关键词 E-预不变凸函数 Hermite-Hadamard型积分不等式 HOLDER不等式 幂平均不等式
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Henig Efficiency in Vector Optimization with Nearly Cone-subconvexlike Set-valued Functions 被引量:8
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作者 Qiu-sheng Qiu 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2007年第2期319-328,共10页
In this paper, we study Henig efficiency in vector optimization with nearly cone-subconvexlike set-valued function. The existence of Henig efficient point is proved and characterization of Henig efficiency is establis... In this paper, we study Henig efficiency in vector optimization with nearly cone-subconvexlike set-valued function. The existence of Henig efficient point is proved and characterization of Henig efficiency is established using the method of Lagrangian multiplier. As an interesting application of the results in this paper, we establish a Lagrange multiplier theorem for super efficiency in vector optimization with nearly conesubconvexlike set-valued function. 展开更多
关键词 set-valued function vector optimization Lagrangian multiplier theorem Henig efficiency nearly cone-subconvexlikeness
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Approximate Weak Minimal Solutions of Set-Valued Optimization Problems
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作者 S.Khoshkhabar-amiranloo 《Journal of the Operations Research Society of China》 EI CSCD 2023年第3期673-692,共20页
This paper deals with approximate weak minimal solutions of set-valued optimization problems under vector and set optimality criteria.The relationships between various concepts of approximate weak minimal solutions ar... This paper deals with approximate weak minimal solutions of set-valued optimization problems under vector and set optimality criteria.The relationships between various concepts of approximate weak minimal solutions are investigated.Some topological properties and existence theorems of these solutions are given.It is shown that for set-valued optimization problems with upper(outer)cone-semicontinuous objective values or closed objective maps the approximate weak minimal and strictly approximate lower weak minimal solution sets are closed.By using the polar cone and two scalarization processes,some necessary and sufficient optimality conditions in the sense of vector and set criteria are provided. 展开更多
关键词 set-valued optimization Approximate weak minimal solutions Existence theorems Optimality conditions Scalarization functions
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The Approximation Theorem of Convolution Operator in △~p Set-valued Function Space
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作者 Pei-xin YeInstitute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Science, Beijing 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2002年第3期495-500,共6页
The paper is a contribution to the problem of approximating random set with values in a separable Banach space. This class of set-valued function is widely used in many areas.We investigate the properties of p-bounded... The paper is a contribution to the problem of approximating random set with values in a separable Banach space. This class of set-valued function is widely used in many areas.We investigate the properties of p-bounded integrable random set. Based on this we endow it with △p metric which can be viewed as a integral type hausdorff metric and present some approximation theorem of a class of convolution operators with respect to △p metric. Moreover we also can establish analogous theorem for other integral type operator in △p space. 展开更多
关键词 set-valued function random set convolution operator △~p space approximation theorem
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强预不变凸函数 被引量:37
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作者 颜丽佳 刘芙萍 《重庆师范大学学报(自然科学版)》 CAS 2005年第1期11-15,共5页
预不变凸函数是凸函数的重要推广函数之一,它在数学规划中有许多的应用。本文在给出一类特殊的预不变凸函数———强预不变凸函数定义的基础上,举例说明这类函数的存在性,并讨论了它和强不变凸函数之间的关系,另外还给出了它的一些基本... 预不变凸函数是凸函数的重要推广函数之一,它在数学规划中有许多的应用。本文在给出一类特殊的预不变凸函数———强预不变凸函数定义的基础上,举例说明这类函数的存在性,并讨论了它和强不变凸函数之间的关系,另外还给出了它的一些基本性质和等价命题。 展开更多
关键词 不变凸函数 等价命题 数学规划 存在性 基本性质 推广 举例 定义 基础 应用
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强预不变凸函数的充要条件(英文) 被引量:12
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作者 唐万梅 杨新民 《运筹学学报》 CSCD 北大核心 2006年第3期50-58,共9页
本文讨论了强预不变凸函数与预不变凸函数、严格预不变凸函数及半严格预不变凸函数之间的关系,得到它的三个充要条件:(i)在一定条件下,f是强预不变凸函数的充分必要条件是f是预不变凸函数且f满足中间点强预不变凸性;(ii)在一定条件下,... 本文讨论了强预不变凸函数与预不变凸函数、严格预不变凸函数及半严格预不变凸函数之间的关系,得到它的三个充要条件:(i)在一定条件下,f是强预不变凸函数的充分必要条件是f是预不变凸函数且f满足中间点强预不变凸性;(ii)在一定条件下,f是强预不变凸函数的充分必要条件是f是严格预不变凸函数且f满足中间点强预不变凸性;(iii)在一定条件下,f是强预不变凸函数的充分必要条件是f是半严格预不变凸函数且f满足中间点强预不变凸性. 展开更多
关键词 运筹学 数学规划 强预不变凸函数 预不变凸函数 严格预不变凸函数 半严格预不变凸函数
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严格预不变凸函数的两个性质(英文) 被引量:7
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作者 彭建文 杨新民 《运筹学学报》 CSCD 北大核心 2005年第1期37-42,共6页
我们考虑了由杨和李在[2]中引入的严格预不变凸函数,并得到了严格预不变凸函数的两个性质,这些性质包括与中间点严格预不变凸性和预不变凸函数有关的一个充分条件以及与半严格预不变凸函数和中间点严格预不变凸性有关的一个等价条件.
关键词 不变凸函数 等价条件 中间点 凸性 充分条件 性质 个性
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