On Semi-(B,G)-Preinvex Functions

We firstly construct a concrete semi-invex set which is not invex. Basing on concept of semi-invex set, we introduce some kinds of generalized convex functions, which include semi-(B,G)-preinvex functions, strictly semi-(B,G)-preinvex functions and explicitly semi-(B,G)-preinvex functions. Moreover,...

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Main Authors: Xiaoling Liu, D. H. Yuan
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/530468
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author Xiaoling Liu
D. H. Yuan
author_facet Xiaoling Liu
D. H. Yuan
author_sort Xiaoling Liu
collection DOAJ
description We firstly construct a concrete semi-invex set which is not invex. Basing on concept of semi-invex set, we introduce some kinds of generalized convex functions, which include semi-(B,G)-preinvex functions, strictly semi-(B,G)-preinvex functions and explicitly semi-(B,G)-preinvex functions. Moreover, we establish relationships between our new generalized convexity and generalized convexity introduced in the literature. With these relationships and the well-known results pertaining to common generalized convexity, we obtain results for our new generalized convexities. We extend the existing results in the literature.
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spelling doaj-art-4da7a63693ed4e76aa433f584dafd2582025-08-20T02:38:45ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/530468530468On Semi-(B,G)-Preinvex FunctionsXiaoling Liu0D. H. Yuan1Department of Mathematics, Hanshan Normal University, Chaozhou, Guangdong 521041, ChinaDepartment of Mathematics, Hanshan Normal University, Chaozhou, Guangdong 521041, ChinaWe firstly construct a concrete semi-invex set which is not invex. Basing on concept of semi-invex set, we introduce some kinds of generalized convex functions, which include semi-(B,G)-preinvex functions, strictly semi-(B,G)-preinvex functions and explicitly semi-(B,G)-preinvex functions. Moreover, we establish relationships between our new generalized convexity and generalized convexity introduced in the literature. With these relationships and the well-known results pertaining to common generalized convexity, we obtain results for our new generalized convexities. We extend the existing results in the literature.http://dx.doi.org/10.1155/2012/530468
spellingShingle Xiaoling Liu
D. H. Yuan
On Semi-(B,G)-Preinvex Functions
Abstract and Applied Analysis
title On Semi-(B,G)-Preinvex Functions
title_full On Semi-(B,G)-Preinvex Functions
title_fullStr On Semi-(B,G)-Preinvex Functions
title_full_unstemmed On Semi-(B,G)-Preinvex Functions
title_short On Semi-(B,G)-Preinvex Functions
title_sort on semi b g preinvex functions
url http://dx.doi.org/10.1155/2012/530468
work_keys_str_mv AT xiaolingliu onsemibgpreinvexfunctions
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