( , ) ρ Φ − invexity has recently been introduced with the intent of generalizing invex functions in mathematical programming. Using such conditions we obtain new sufficiency results for optimality in multiobjective programming and extend some classical duality properties.

In this paper, a generalization of convexity, namely V -rinvexity, is considered in the case of nonlinear multiobjective programming problems where the functions involved are differentiable. The assumptions on Pareto solutions are relaxed by means of V -r-invex functions. Also some duality results are obtained for such optimization problems.

1 Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia 2 Department of Mathematical Sciences, Florida Institute of Techynology, Melbourne 32901, USA 3 Department of Mathematics, Aligarh Muslim University, Aligarh-202 002, India 4 Department of Mathematics, Faculty of Applied Sciences, Integral University, Lucknow 226026, India 5 D...

In this paper, several kinds of invariant monotone maps and generalized invariant monotone maps are introduced. Some examples are given which show that invariant monotonicity and generalized invariant monotonicity are proper generalizations of monotonicity and generalized monotonicity. Relationships between generalized invariant monotonicity and generalized invexity are established. Our results...