To globalize the Newton method and closely approximate the solution q* of (2.3), we use a continuation scheme in γ where we iteratively solve the problem for an increasing sequence γ n, using the previous solution as initial guess.
The "sequence duration" categories were set using an increasing width of the sequence with increasing average duration as also used in several posture studies [ 29].
In the present paper, we have generalized this theorem on the φ − | A, p n | k summability factors under weaker conditions by using an almost increasing sequence instead of a positive non-decreasing sequence.
In this paper, we generalize a known theorem dealing with | C, 1 | k summability factors to the | C, α | k summability factors of infinite series using an almost increasing sequence.
Using an increased amount of sequence data we test between alternative hypotheses of soft polytomies caused by rapid speciation, slow evolutionary rate and/or insufficient sequence data, and hard polytomies caused by simultaneous speciation within this family.
Recently, Rhoades and Savaş [1] obtained sufficient conditions for to be summable, by using almost increasing sequence.
Because LncRNAs have a higher mutation rate than protein coding sequences [ 14, 22], the analysis was done using increasing sequence similarity cut-off values of ≥10 %, ≥20 % and ≥50%%.
In this study, we have generalized a well-known theorem dealing with an absolute summability method to a ({varphi}-|T,p_{n}|_{k}) summability method of an infinite series by using almost increasing sequences and δ-quasi-monotone sequences.
We prove two theorems on,, summability factors for an infinite series by using quasi-power increasing sequences.
In this paper, we prove a general theorem dealing with absolute Cesàro summability factors of infinite series by using a quasi-f-power increasing sequence instead of a quasi-σ-power increasing sequence.
Among them, Bor and Özarslan have proved two theorems for | N ¯, p n | k summability method by using quasi β-power increasing sequence [5].
