Sentence examples for mappings and c from inspiring English sources

Proof Taking S i = P C i, T i = P Q i, and K i = P i, i = 1, 2, … in Theorem 3.3, we know that S i and T i both are nonexpansive with F ( S i ) = C i and F ( T i ) = Q i and so they are quasi-nonexpansive mappings, and C = ⋂ i = 1 ∞ F ( S i ) and Q = ⋂ i = 1 ∞ F ( T i ).

For every (i=1,2,ldots, N), let (T_{i}: C rightarrow C) be nonexpansive mappings and (T: C rightarrow C) be a ρ-strictly pseudononspreading mapping for some (rhoin[0,1)).

Let S, T : C → C be nonexpansive mappings and Γ : C → C be a ζ-strictly pseudocontractive mapping with ζ ∈ [ 0, 1 ).

For every (i=1,2,ldots, N), let (T_{i}: C rightarrow C) be (kappa _{i} -strict pseudo-contractive mappings and (T: C rightarrow C) be a ρ-strictly pseudononspreading mapping for some (rhoin[0,1)).

Let h : C → C be a α-contraction mapping, T : C → C and S : K → K be non-expansive mappings and f : C × C → R and g : K × K → R be bi-functions satisfying the conditions (A1 - A4).

Let T : C → C and S : K → K be non-expansive mappings and f : C × C → R and g : K × K → R be bi-functions satisfying the conditions (A1 - A4).

For every (i=1,2,ldots, N), let (B_{i}: C rightarrow H) be (xi _{i} -inverse-strongly monotone mappings and (T: C rightarrow C) be a ρ-strictly pseudononspreading mapping for some (rhoin[0,1)).

where T i : C i → E, i = 1, 2,..., N is nonexpansive nonself-mapping and C i is a closed convex sunny nonexpansive retract of E. Lemma 3.8.

Let E be a uniformly convex Banach space, C be a nonempty closed convex subset of E, and let T1, T2 : C → C be two nonexpansive mappings, and let S: C → C be a mapping with condition (C).

Let E be a uniformly convex and uniformly smooth Banach space with Opial's condition, C be a nonempty closed convex subset of E, and let T1, T2 : C → C be two nonexpansive mappings, and let S: C → C be a mapping with condition (C).

Let E be a uniformly convex Banach space with Opial's condition, C be a nonempty closed convex subset of E, and let T1, T2 : C → C be two nonexpansive mappings, and let S: C → C be a mapping with condition (C).