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
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
A class of sets called E-invex sets and a class of functions called E-preinvex functions,semi-E-preinvex functions and generalized semi-E-preinvex functions are introduced.They are the generalizations of E-convex sets...A class of sets called E-invex sets and a class of functions called E-preinvex functions,semi-E-preinvex functions and generalized semi-E-preinvex functions are introduced.They are the generalizations of E-convex sets,E-convex functions and semi-E-convex functions respectively,also the generalizations of invex sets and preinvex functions.Furthermore some optimality results of mathematical programming problems involved semi-E-preinvex functions and generalized semi-E-preinvex functions are obtained.展开更多
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.
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
基金Supported by the National Natural Science Foundation of China(Grant No.11801342)the Natural Science Foundation of Shaanxi Province(Grant No.2023-JC-YB-043).
文摘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.
基金The NSF(11801342) of Chinathe Foundation(18JK0116) of Shaanxi Educational Committee
文摘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.
基金Supported by Key Disciplines of Shanghai Municipality（Operations Research and Cybernetics）（S30104） Supported by Shanghai Leading Academic Discipline Project（J50101） Supported by National Science Foundation Project of CQCSTC（2009BB3372）
文摘A class of sets called E-invex sets and a class of functions called E-preinvex functions,semi-E-preinvex functions and generalized semi-E-preinvex functions are introduced.They are the generalizations of E-convex sets,E-convex functions and semi-E-convex functions respectively,also the generalizations of invex sets and preinvex functions.Furthermore some optimality results of mathematical programming problems involved semi-E-preinvex functions and generalized semi-E-preinvex functions are obtained.
基金Supported by the National Natural Science Foundation of China (10571035)
文摘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.
基金Project supported by the National Natural Science Foundation of China (No. 10371024) the Natural Science Foundation of Zhejiang Province (No.Y604003)
文摘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.
基金This research was partially supported by the National Natural Science Foundation of China(Grant No.10171118,10471159)the key project of the Chinese Ministry of Education,Supported by Program for New Century Excellent Talents in University.
