Remark 6 It is clear that each generalized locally convex space is an generalized uniform space.
In addition, we address the problem of routing of messages in an generalized linear recursive network (GLRN).
Ono et al.: In 2014, Ono et al. [22] proposed a cartoon-texture decomposition using the block nuclear norm (an generalized version of [23]) which interprets the texture component as the combination of overlapped and sheared blockwise low-rank matrices in different directions.
(6) T is said to be an generalized asymptotically quasi- ϕ -nonexpansive mapping if F ( T ) ≠ ∅, and there exist two nonnegative sequences {μ n } ⊂ [0, ∞) with μ n → 0, and {ξ n } ⊂ [0, ∞) with ξ n → 0 as n→∞ such that ϕ ( p, T n x ) ≤ ( 1 + μ n ) ϕ ( p, x ) + ξ n, ∀ x ∈ C, p ∈ F ( T ), n ≥ 1. .
T is said to be an generalized asymptotically quasi- ϕ -nonexpansive mapping if F ( T ) ≠ ∅, and there exist two nonnegative sequences {μ n } ⊂ [0, ∞) with μ n → 0, and {ξ n } ⊂ [0, ∞) with ξ n → 0 as n→∞ such that ϕ ( p, T n x ) ≤ ( 1 + μ n ) ϕ ( p, x ) + ξ n, ∀ x ∈ C, p ∈ F ( T ), n ≥ 1. Remark 2.6.
If a mapping (Omega ^m_3:X^3timathbb3times X^3rightarrow mathbb {R}^+) is given by begin{aligned} Omega ^m_3 X,U,A =max {G x,u,a),G y,v,b),G z,w,c }, end{aligned} for all (X= x,y,z),U= u,v,w)) and (A= a,b,c in X ^3,) then ((X^3,Omega ^m_3)) is an generalized (b -metric space (with the same parameter (s)).
