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Indeed, if W ( 0 ) ∈ E p, the connectivity will stay in E p, in particular 0 < L − W ≤ L along the trajectories, more precisely L − W is a strictly positive constant since p ∈ ] 0, 1 [. Because v ¯ is also bounded by u m l ( 1 − p ), v ¯ ⋅ v ¯ ′ + σ 2 2 ( L − W ) − 1 is bounded.
More precisely, L p is min { p, 2 } -uniformly smooth for every p > 1.
More precisely, L p is min{p, 2}-uniformly smooth for every p > 1. Definition 2.1.
More precisely, L p is min { p, 2 } -uniformly smooth and uniformly convex for every p ≥ 1.
More precisely, L p is min{p, 2}-uniformly smooth for every p > 1. Lemma 2.1.(Zhou [37]) Let E be a real 2-uniformly smooth Banach space with the best smooth constant K, C be a nonempty subset of E, and let T : C → C be a λ-strict pseudocontraction.
More precisely, L p is min { p, 2 } -uniformly smooth for every p > 1. Recall that a mapping S is said to be λ-strictly pseudocontractive iff there exist a constant λ ∈ ( 0, 1 ) and j ( x − y ) ∈ J ( x − y ) such that 〈 S x − S y, j ( x − y ) 〉 ≤ ∥ x − y ∥ 2 − λ ∥ ( I − S ) x − ( I − S ) y ∥ 2 ∀ x, y ∈ C. (2.2).
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