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Some Properties of (F, K)-Convex Mappings

Author: LiuYuHui
Tutor: ZuoZuo
School: Northeast Forestry University
Course: Applied Mathematics
Keywords: ( F , K ) - convex set ( F , K ) - convex mapping ( F , K ) - Preinvexity convex mapping Half - ( F , K ) - Preinvexity convex mapping
CLC: O174.13
Type: Master's thesis
Year: 2011
Downloads: 4
Quote: 0
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Abstract


The optimization theory both optimization is an important part of an important theoretical basis and operations research . Optimization theory as the basic nature - convex sets and convex mapping has wide application in many other areas of mathematics , has practical significance to promote the collection and Convex Function . Youness 1999 introduced the concept of E - convex set and E- convex function , Yang Xinming and Chen Xiusu , then gives the definition and properties of semi -E- convex function , at the same time Hanson defined preinvex function . This paper introduces the ( F , K ) - convex sets ( F , K ) the - convex mapped , ( F , K ) - invariant convex sets ( F , K ) - Preinvexity the concept of convex mapping , and discuss the nature of . In recent decades , research tools - set-valued analysis and convex analysis optimization theory and so have made great progress , for the generalized convexity research provides new ideas, new methods , achieved many useful conclusions , which also to promote more generally, within the framework of generalized convexity theory become the focus of domestic and foreign scholars . In this paper consists of two parts : The first part, based on the definition of E - convex set and E- convex function , as well as semi -E- convex sets and semi -E - convex function , convex analysis , functional analysis and set value analysis for the study of tools to promote the concept to set the value of the case , given ( F , K ) - convex sets ( F , K ) - convex mapping and a half - ( F , K ) - convex mapping defined on the nature of the research . The second part of the definition of semi -E- invariant convex sets and semi -E- pre- invex functions based on the introduction of ( F , K ) - invariant convex set , ( F , K ) - preinvex mapping and a half - ( F , K ) - preinvexity the convex mapping concept and discusses a number of properties of E- invariant convex sets and E- invariant convex function .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Theory of functions > Real Analysis,Real Variable > Convex function, convex set theory
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