Generalized (α, Β, Γ, Η, Ρ, Θ)-invex Functions in Semiinfinite Fractional Programming. Part I: Sufficient Optimality Conditions

subject to Gj(x, t) ≤ 0 for all t ∈ Tj , j ∈ q, Hk(x, s) = 0 for all s ∈ Sk, k ∈ r, x ∈ X, where q and r are positive integers, X is a nonempty open convex subset of Rn (n-dimensional Euclidean space), for each j ∈ q ≡ {1, 2, . . . , q} and k ∈ r, Tj and Sk are compact subsets of complete metric spaces, f and g are real-valued functions defined on X, for each j ∈ q, z → Gj(z, t) is a real-valued function defined on X for all t ∈ Tj , for each k ∈ r, z → Hk(z, s) is a real-valued function defined on X for all s ∈ Sk, for each j ∈ q and k ∈ r, t → Gj(x, t) and s→ Hk(x, s) are continuous real-valued functions defined, respectively, on