The Study Higher-order Wolfe-type Non-differentiable Multiple Objective Symmetric Duality Involving Generalized Convex Functions

In this paper, a new class of generalized $$K-({\Phi}{,{\rho}})$$ K - ( Φ , ρ ) convex function is introduced, in which the sublinearity property of F as in literature is relaxed by imposing the convexity assumption on $$\phi$$ ϕ in its third argument with an example. This new class of generalized convex function is more generalized than the $$(F,\alpha ,\rho ,d)$$ ( F , α , ρ , d ) -convex functions, $$(C,\alpha ,\rho ,d)$$ ( C , α , ρ , d ) -convex functions and $$K-(F,\alpha ,\rho ,d)$$ K - ( F , α , ρ , d ) convex functions studied in literature. Also, a new model of higher-order Wolfe-type non-differentiable multi-objective symmetric dual programs is presented and the weak, strong, and converse duality theorem under higher-order $$K-({\Phi}{,{\rho}})$$ K - ( Φ , ρ ) convex functions are established. Some special cases which generalizes our results is discussed.