(α, β, λ, δ, m, Ω)p−Neighborhood for some families of analytic and multivalent functions
Abstract In the present investigation, we give some interesting results related with neighborhoods of p−valent functions. Relevant connections with some other recent works are also pointed out.
Coefficient inequalities and inclusion relations for some families of analytic and multivalent functions
Abstract By means of the derivative operator of order m ( m ∈ N 0 ), we introduce and investigate two new subclasses of p -valently analytic functions of complex order. The various results obtained here for each of these two function classes include coefficient inequalities and inclusion relationships involving the ( n , δ ) -neighborhood of p -valently analytic functions. Relevant connections with some other recent investigations are also pointed out.
A new class of numerical sequences and its applications to sine and cosine series
First, it is proved that the class of classical quasi-monotone sequences is not comparable to the newly defined class of sequences of ‘rest bounded variation’. Considering this result, we prove three sample theorems for sequences of rest bounded variation, being analogues of the theorems proved earlier for monotone or quasi-monotone sequences. One of them gives a partial answer to a question raised by R. P. Boas Jr.