In this paper, a class of functions, named as r-semipreinvex functions, which is generalization of semipreinvex functions and r-preinvex functions, is introduced. Example is given to show that there exists function wh...
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In this paper, a class of functions, named as r-semipreinvex functions, which is generalization of semipreinvex functions and r-preinvex functions, is introduced. Example is given to show that there exists function which is r-semipreinvex function, but is not semipreinvex function. Furthermore, some basic characterizations of r-semipreinvex functions are established. At the same time, some optimality results are obtained in nonlinear programming problems.
In this paper, a new class of functions called semi-G-preinvex functions, which is generalization of semipreinvex functions and G-preinvex functions, is introduced. Some examples are given to show that there exist fun...
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In this paper, a new class of functions called semi-G-preinvex functions, which is generalization of semipreinvex functions and G-preinvex functions, is introduced. Some examples are given to show that there exist functions which are semi-G-preinvex functions, but are not G-invex functions, semipreinvex functions and G-preinvex functions. Furthermore, some interesting properties and characterizations of semi-G-preinvexity are established. Our results extend and improve the corresponding ones in the literature.
In this note, a class of functions, called semi-B-preinvex function, which are a generalization of the semipreinvex functions and the B-vex functions, is introduced. Examples are given to show that there exist functio...
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In this note, a class of functions, called semi-B-preinvex function, which are a generalization of the semipreinvex functions and the B-vex functions, is introduced. Examples are given to show that there exist functions which are semi-B-preinvex functions, but are neither semipreinvex nor B-vex. A property of the semi-B-preinvex functions is obtained.
In this paper, we study some properties of a class of nonconvex functions, called semipreinvex functions, which includes the classes of preinvex functions and are-connected convex functions. It is shown that the minim...
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In this paper, we study some properties of a class of nonconvex functions, called semipreinvex functions, which includes the classes of preinvex functions and are-connected convex functions. It is shown that the minimum of an arcwise directionally differentiable semi-invex functions on a semi-invex set can be characterized by a class of variational inequalities, known as variational-like inequalities. We use the auxiliary principle technique to prove the existence of a solution of a variational-like inequality and suggest a novel iterative algorithm.
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