"Killing," for instance, rather brilliantly connects respect for life to respect for the art of living, on the most secular terms.
In this way, privacy is also closely connected with respect and self respect.
This means that φ is ρ-generalized-pseudo-right upper-Dini-derivative locally arcwise connected (with respect to H) at x ¯ = 0.
The function φ : X → R is said to be ρ-generalized-quasi-right upper-Dini-derivative locally arcwise connected (with respect to H) on X if it is ρ-generalized-quasi-right upper-Dini-derivative locally arcwise connected (with respect to H) at any x ¯ ∈ X.
The function φ : X → R is said to be ρ-generalized-pseudo-right upper-Dini-derivative locally arcwise connected (with respect to H) on X if it is ρ-generalized-pseudo-right upper-Dini-derivative locally arcwise connected (with respect to H) at any x ¯ ∈ X.
∑ i = 1 s ∗ λ i ∗ f ( ⋅, y ∗ i ) is strictly ρ ¯ -generalized-pseudo-right upper-Dini-derivative locally arcwise connected (with respect to H) at z ∗, ∑ j = 1 m μ j ∗ g j is ρ ˘ -generalized-quasi-right upper-Dini-derivative locally arcwise connected (with respect to H) at z ∗, ρ ¯ ( x ∗, z ∗ ) + ρ ˘ ( x ∗, z ∗ ) ≥ 0. Then z ∗ = x ∗.
Also, assume that (i) ∑ i = 1 s λ i f ( ⋅, y i ) is strictly ρ ¯ -generalized-pseudo-right upper-Dini-derivative locally arcwise connected (with respect to H) at x ¯, (ii) ∑ j = 1 m μ j g j is ρ ˘ -generalized-quasi-right upper-Dini-derivative locally arcwise connected (with respect to H) at x ¯, (iii) ρ ¯ ( x, x ¯ ) + ρ ˘ ( x, x ¯ ) ≥ 0. .
Assume that (i) ∑ i = 1 s λ i f ( ⋅, y i ) is ρ ¯ -generalized-pseudo-right upper-Dini-derivative locally arcwise connected (with respect to H) at z, (ii) ∑ j = 1 m μ j g j is ρ ˘ -generalized-quasi-right upper-Dini-derivative locally arcwise connected (with respect to H) at z, (iii) ρ ¯ ( x, z ) + ρ ˘ ( x, z ) ≥ 0. .
Also, assume that (i) ∑ i = 1 s ∗ λ i ∗ f ( ⋅, y ∗ i ) is strictly ρ ¯ -generalized-pseudo-right upper-Dini-derivative locally arcwise connected (with respect to H) at z ∗, (ii) ∑ j = 1 m μ j ∗ g j is ρ ˘ -generalized-quasi-right upper-Dini-derivative locally arcwise connected (with respect to H) at z ∗, (iii) ρ ¯ ( x ∗, z ∗ ) + ρ ˘ ( x ∗, z ∗ ) ≥ 0. .
Also, assume that (i) ∑ i = 1 s λ i f ( ⋅, y i ) is ρ ¯ -generalized-pseudo-right upper-Dini-derivative locally arcwise connected (with respect to H) at x ¯, (ii) ∑ j = 1 m μ j g j is ρ ˘ -generalized-quasi-right upper-Dini-derivative locally arcwise connected (with respect to H) at x ¯, (iii) ρ ¯ ( x, x ¯ ) + ρ ˘ ( x, x ¯ ) ≥ 0. .
