This paper studies the convex multiobjective optimization problem with vanishing constraints‎. ‎We introduce a new constraint qualification for these problems‎, ‎and then a necessary optimality condition for properly efficient solutions is presented‎. ‎Finally by imposing some assumptions‎, ‎we show that our necessary condition is also sufficient for proper efficiency‎. ‎Our results are formula...

Abstract Although the isogeometric collocation (IGA-C) method has been successfully utilized in practical applications due to its simplicity and efficiency, only a little theoretical results have established on numerical analysis of IGA-C method. In this paper, we deduce convergence rate consistency Moreover, based formula rate, necessary sufficient condition for is developed. These advance

Abstract: In the present paper, we give a necessary and sufficient condition for contact CR-warped product to be contact CR-product in Kenmotsu space forms.

A necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

abstract: in the present paper, we give a necessary and sufficient condition for contact cr-warped product to be contact cr-product in kenmotsu space forms.