A class of -semipreinvex functions, which are some generalizations of the semipreinvex functions, and the -convex functions, is introduced. Examples are given to show their relations among -semipreinvex functions, semipreinvex functions and -convex functions. Some characterizations of -semipreinvex functions are also obtained, and some optimality results are given for a class of -semipreinvex functions. Ours results improve and generalize some known results.
Xue Wen Liu. Ke Quan Zhao. Zhe Chen. "A Class of -Semipreinvex Functions and Optimality." J. Appl. Math. 2012 (SI15) 1 - 12, 2012. https://doi.org/10.1155/2012/168172