id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-619	Gulati, T. R.; Saini, Himani	Higher-order (F,alpha,beta,rho,d)-Convexity and its Application in Fractional Programming	2011	10	.pdf	application/pdf	3102	227	76	A functional F : X × X ×Rn 7→ R is said to be sublinear in the third variable, if for all x , x̄ ∈ X , (i) F(x , x̄ ;ξ1 + ξ2)≦ F(x , x̄;ξ1) + F(x , x̄ ;ξ2), for all ξ1,ξ2 ∈ Rn ; and (ii) F(x , x̄ ;αa) The function φ is said to be higher-order (F,α,β ,ρ, d)-convex at x̄ with respect to K , if for all x ∈ X and p ∈ Rn, φ(x)−φ( x̄) ≧ F(x , x̄ ;α(x , x̄){∇φ( x̄) +∇pK( x̄ , p)}) + β(x , x̄){K( x̄ , p)− pT∇pK( x̄ , p)}+ρd2(x , x̄).	cache/ejpam-619.pdf	txt/ejpam-619.txt