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Proof Note that E ↪ L 1.

Proof Note that γ ≤ α, β.

Proof Note that γ satisfies the relation 0 < γ < 1.

Proof: Note that (i) and (ii) are equivalent.

Proof Note that the induced cycle C 4 σ of G σ must be negative.

Proof Note that Θ is an L φ -averaging domain and φ is doubling.

Proof Note that h = h fulfils (1.20) if η ¯ ∈ K in view of Theorem 4.1.

Proof Note first that by Lemmas 1 and 2, h ( n ) is a divergent sequence.

Proof Note that M { | ξ | ≥ f − 1 ( r ) } is a decreasing function of r on [ 0, + ∞ ).

Proof Note that f is G-preinvex on X with respect to η.

Proof Note that any tree T has diameter d ≥ 3 if T ≇ S n.