M.K. Aouf's research while affiliated with Mansoura University and other places

The purpose of the present paper is to introduce subclasses of $$p-$$ p - valent functions defined by linear operator. Inclusion relationships for functions in these subclasses are discussed.

The object of this paper is to derive various properties and characters for a class of p-valently Bazileviˇ c functions defined with higher order derivatives. Using the technique of Briot-Bouquet differential subordination we obtained several results, some of them presented here generalize and improve a few earlier results, and several others are new ones involving differential inequalities. These last implications deal with the symmetric open disc and symmetric conic domains with respect to the real axe. Our results extends and improves many other previous ones, and some of them are the best possible under the given assumptions.

We introduce a new class of analytic functions with negative coefficients by using the $q-$analogue of multiplier transformation operator. Coefficient inequalities, distortion theorems, closure theorems, and some properties involving the modified Hadamard products, radii of close-to-convexity, starlikeness, and convexity, and integral operators associated with functions belonging to this class are obtained.

In this paper, we investigate a subclass \(L(q,b,\alpha ,t)\) by means of Chebyshev polynomials and \(q-\) derivative operator expansions of univalent functions of complex order in the open unit disk. Later, we find initial coefficients \(|a_{2}|\)and \(|a_{3}|\) and sharp bounds of Fekete–Szegő functional \(|a_{3}-\xi a_{2}^{2}|\) for functions in this subclass.

In this paper, we obtain the necessary and sufficient conditions for generalized Bessel functions of the first kind zup(z) to be in the classes S(b, λ, β) and R(b, λ, β) of analytic functions with complex order and also give the necessary and sufficient conditions for z(2−up(z)) to be in the classes TS(b, λ, β) and TR(b, λ, β). Furthermore, we give the necessary and sufficient conditions for J(k, c) to be in the class TR(b, λ, β) provided that the function f is in the class Rτ (A, B). Finally, we give conditions for the integral operator G(k, c, z) = ∫0z(2 − up(t))dt to be in the class TR(b, λ, β). Several corollaries and consequences of the main results are also obtained.

We establish coefficient bounds for functions from the subclasses of p-valent starlike and p-valent convex functions defined by higher-order derivatives and complex order introduced with the help of a certain nonhomogeneous Cauchy–Euler differential equation with higher-order derivatives. Relevant connections of some of our results with the results obtained earlier are provided.

In this paper we study convolution properties of spirallike multivalent functions defined by using a differential operator and higher order derivatives. Using convolution product relations we determine necessary and sufficient conditions for multivalent functions to belong to these classes, and our results generalized many previous results obtained by different authors. We obtain convolution and inclusion properties for new subclasses of multivalent functions defined by using the Dziok-Srivatava operator. Moreover, using a result connected with the Briot-Bouquet differential subordination, we obtain an inclusion relation between some of these classes of functions.

UDC 517.5 We determine coefficient bounds for functions from subclasses of p -valent starlike and p -valent convex functions defined by higher-order derivatives and complex order introduced with the help of a certain nonhomogeneous Cauchy – Euler differential equation for higher-order derivatives. Relevant connections of some of our results with the results obtained earlier are provided.

In the present paper, we investigate and introduce several properties of certain families of analytic functions in the open unit disc, which are defined by q -analogue of Mittag-Leffler function associated with conic domain. A number of coefficient estimates of the functions in these classes have been obtained. Sufficient conditions for the functions belong to these classes are also considered.

This paper studies some inclusion properties of some new subclasses of analytic functions in the open symmetric unit disc U that are associated with the Pascal operator. Furthermore, the integral-preserving properties in a sector for these subclasses are also investigated.