Strong convergence for total quasi-φ-asymptotically nonexpansive semigroups in Banach spaces
نویسندگان
چکیده
Definition . Let T : C → C be a mapping. T is said to be total asymptotically nonexpansive if there exist sequences {μn}, {νn} with μn,νn → as n → ∞ and a strictly increasing continuous function ψ : R → R with ψ() = such that ‖Tnx – Tny‖ ≤ ‖x – y‖ +μnψ(‖x – y‖) + νn holds for all x, y ∈ C and all n ∈N. T is said to be total asymptotically quasi-nonexpansive if F(T) = ∅, there exist sequences {μn}, {νn}withμn,νn → as n→∞ and a strictly increasing continuous functionψ :R→ R with ψ() = such that ‖Tnx – p‖ ≤ ‖x – p‖ +μnψ(‖x – p‖) + νn holds for all x ∈ C, p ∈ F(T) and all n ∈N.
منابع مشابه
Total quasi-φ-asymptotically nonexpansive semigroups and strong convergence theorems in Banach spaces
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