Sentence examples for be two bifunctions of from inspiring English sources

Theorem 3.1 Let C be a nonempty closed convex subset of a real Hilbert space H, Φ 1 and Φ 2 be two bifunctions of C × C into R satisfying (A 1 -(A 4).

Theorem 3.3 Let C be a nonempty closed convex subset of a real Hilbert space H and Φ 1 and Φ 2 be two bifunctions of C × C into R satisfying (A 1 -(A 4).

Corollary 3.3 Let H be a real Hilbert space, C be a closed convex subset of H. Let F 1, F 2 be two bifunctions of C × C into R satisfying (A 1 -(A 4) and B, B 1, B 2 : C → H be β, η, ρ -inverse-strongly monotone mappings, ψ 1, ψ 2 : C → R be convex and lower semicontinuous function.

Corollary 3.7 Let H be a real Hilbert space, C be a closed convex subset of H. Let F 1, F 2 be two bifunctions of C × C into R satisfying (A 1 -(A 4) and B 1, B 2 : C → H be η, ρ -inverse-strongly monotone mappings, ψ 1, ψ 2 : C → R be convex and lower semicontinuous function, f : C → C be a contraction with coefficient α ( 0 < α < 1 ).

Corollary 3.2 Let H be a real Hilbert space, C be a closed convex subset of H. Let F 1, F 2 be two bifunctions of C × C into R satisfying (A 1 -(A 4) and B, B 1, B 2 : C → H be β, η, ρ -inverse-strongly monotone mappings, ψ 1, ψ 2 : C → R be convex and lower semicontinuous function, f : C → C be a contraction with coefficient α ( 0 < α < 1 ), M : H → 2 H be a maximal monotone mapping.

Let C be a nonempty, closed, and convex subset of H and let F and G be two bifunctions from (Ctimes C) to R which satisfies (A1 - A4).

Theorem 4.8 Let H be a Hilbert space, let C be a nonempty closed convex subset of H. Let F 1 and F 2 be two bifunctions from C × C into ℝ satisfying (A1 - A4), respectively.

Let C be a nonempty closed convex subset of H, (varphi Ctimes Crightarrowmathbb{R}), and let (F: Ctimes Crightarrowmathbb{R}) be two bifunctions.

Let and be two bifunctions from satisfying (A1)–(A1).

Let and be two bifunctions from into satisfying (A1)–(A4), respectively.

Let and be two bifunctions from to satisfying (A1)–(A1).