Furthermore, by using the same arguments as in Lemmas 2.1 and 2.2, we have the following result.
Furthermore, by using the same techniques as in the proof of Theorem 3.1, we can prove the convexity (univalence) of and so the details may be omitted.
By noting that 0 < ρ ≦ 1 / 2 from (2.2), we obtain from the condition (2.20) that ψ is a close-to-convex function in U (see [24]), and hence ν f is univalent in U. Furthermore, by using the same techniques as in the proof of Theorem 3, we can prove the convexity (univalence) of F and so the details may be omitted.
Since δ given by (2.2) satisfies the inequality 0 < δ ≤ 1 / 2, the condition (2.17) means that ϕ f ( z ) is a close-to-convex function in U (see [20]), and hence ϕ f ( z ) is univalent in U. Furthermore, by using the same techniques as in the proof of Theorem 2.1, we can prove the convexity univalence) of F and so the details may be omitted.
Furthermore, by using the same test, OF50 was compared between the Coombs' positive and Coombs' negative dogs and between the in-saline auto-agglutination positive and negative dogs.
Furthermore, by examining the same young cohort at risk across multiple adverse outcomes, we have found that the gender differentials in criminality incidence rates were far greater than those for mortality and psychiatric morbidity adverse outcomes.
Furthermore, SLiMs recognised by the same motif-binding pocket are typically found in multiple non-homologous proteins (Fig. 1b- d).
Furthermore, a study by the same group demonstrated higher progranulin levels in insulin resistant compared with insulin-sensitive individuals with morbid obesity (7).
Furthermore, it might by the same token dramatically reduce the growing dependence of the elderly on outside assistance in their activities of daily living, whilst effectively promoting greater self-reliance, and – last but not least – significantly boosting up their self-confidence.
