The phrase "also proved the same" is correct and usable in written English.
It can be used when you want to indicate that something has been demonstrated or confirmed in addition to what has already been stated.
Example: "The researchers conducted further experiments, and their findings also proved the same as the initial study."
Alternatives: "also confirmed the same" or "likewise demonstrated the same".
The ultraviolet spectrometer 260-nm light absorption value measurement also proves the same result (data not shown).
Here we modify the result for Ćirić quasi-contraction-type mappings and also prove the same result by taking D-admissible mappings.
The same authors also proved the following result, which will be needed in the sequel.
At the same time, they also proved the existence of infinitely many nonoscillatory solutions for Eq. (1.5).
Then T is ϕ-strongly pseudocontractive if and only if there exists a strictly increasing function Φ : [ 0, + ∞ ) → [ 0, + ∞ ) with Φ ( 0 ) = 0 such that (1.1) holds and lim s → ∞ inf Φ ( s ) s = σ > 0. At the same time, Xiang [1] also proved the following existence theorem.
The same authors also proven the cytotoxic effect of surfactin against the human chronic myelogenous leukaemia cells K562 and the hepatic carcinoma cells BEL7402 2009aa).
Pagacz in [17] has proved the same and also proved that each k-∗-paranormal operator has a Wold-type decomposition.
This paper focuses on an ecosystem model of class-A plant diseases and insect pests to analyze the stability of the equilibrium of the model; it discusses the sufficient condition for the existence of a periodic solution of order one of the system, and at the same time, it also proves the conditions under which the periodic solution is asymptotically stable.
It is also proved that the same inequality holds for the norms in the associated non-commutative Lp spaces when p is an even integer, p⩾d and when the generators of the free group are more generally replaced by ∗-free R-diagonal operators.
