Let 𝑇 ∶ 𝐶 → 𝐻∗

and 𝜂: 𝐶 × 𝐶 → 𝐻 be given mapping. Then the variational like inequality problem is to find

𝑥 ∈ 𝐶 such that

≥ 0, ∀ 𝑦 ∈ 𝐶.

Where H is Hilbert space and H* it's dual.