Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Semilocal E-preinvexity and its applications in nonlinear multiple objective fractional programming | Jiao and Liu Journal of Inequalities and Applications 2011 2011 116 http content 2011 1 116 3 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Semilocal E-preinvexity and its applications in nonlinear multiple objective fractional programming Hehua Jiao1 2 and Sanyang Liu1 Correspondence jiaohh361@126. com department of Mathematics Xidian University Xi an 710071 China Full list of author information is available at the end of the article Springer Abstract Introduction In this paper a new class of functions called semilocal E-preinvex functions is introduced which is generalization of semi-E-preinvex functions and semilocal E-convex functions. Some of its basic properties are obtained. Methods and Materials Using E-h-semidifferentiability some optimality conditions and duality results are established for a nonlinear multiobjective fractional programming with semilocal E-preinvex and related functions. Conclusion The results presented in this paper extend and generalize previously known results in this area. Mathematics Subject Classification 2000 90C26 90C30 90C46 Keywords local E-invex set semilocal E-preinvexity multiobjective fractional programming optimality duality 1. Introduction Convexity and generalized convexity play a vital role in the study of optimality and duality aspects of mathematical programming. Attempts have been made to generalize convexity to study their role in solving such types of problems. Generalizations of convexity related to optimality and duality for nonlinear singleobjective or multiobjective optimization problems have been of much interest in the recent past and many contributions have been made to this development. See . 1-6 and the references therein. After Ewing 7 presented the definition of semilocal convexity by using more general semilocal preinvexity and h-semidifferentiability Preda and Stancu-Minasian 8 gave optimality conditions for weak .
