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Inclusion and neighborhood properties of certain subclasses of p -valent functions of complex order defined by convolution

Rabha El-Ashwah;  Mohamed Aouf;  S. El-Deeb — 2011

Annales UMCS, Mathematica

In this paper we introduce and investigate three new subclasses of p-valent analytic functions by using the linear operator Dmλ,p(f * g)(z). The various results obtained here for each of these function classes include coefficient bounds, distortion inequalities and associated inclusion relations for (n, θ)-neighborhoods of subclasses of analytic and multivalent functions with negative coefficients, which are defined by means of a non-homogenous differential equation.

Inclusion and neighborhood properties of certain subclasses of p-valent functions of complex order defined by convolution

R. M. El-Ashwah;  M. K. Aouf;  S. M. El-Deeb — 2011

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

In this paper we introduce and investigate three new subclasses of p -valent analytic functions by using the linear operator D λ , p m ( f * g ) ( z ) . The various results obtained here for each of these function classes include coefficient bounds, distortion inequalities and associated inclusion relations for ( n , θ ) -neighborhoods of subclasses of analytic and multivalent functions with negative coefficients, which are defined by means of a non-homogenous differential equation.

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