The purpose of this article is to introduce the concept second order (?,?)-invex function for continuous case and apply it discuss duality relations a class multiobjective variational problem. Weak, strong strict theorems are obtained in relate efficient solutions primal problem its Mond-Weir type dual using aforesaid assumption. A non-trivial example also exemplified show presence proposed fun...

In this paper, we consider a multiobjective programming problem with inequality and set constraints. We derive sufficient conditions for the optimality of feasible point under generalized invexity assumptions in terms convexificators. give an example to illustrate that concept convexificators is weaker than other subdifferentials. formulateWolfe Mond-Weir type duals nonsmooth constraints establ...

We prove potential automorphy results for a single Galois representation $$G_F\rightarrow GL_n(\overline{\mathbb {Q}}_l)$$ where F is CM number field. The strategy to use the p, q switch trick go between p-adic and q-adic realisation of certain variant Dwork motive. choose this break self-duality shape motives, but not Hodge-Tate weights. Another key result that representations we come from mot...