On coefficient bounds of a certain class of p

Let Sλ(A,B,p,α)(|λ|<π2, −1≦A<B≦1 and 0≦α<p), denote the class of functions f(z)=zp+∑n=p+1∞anzn analytic in U={z:|z|<1}, which satisfy for z=reiθ∈Ueiλsecλzf′(z)f(z)−ip tanλ=p+[pB+(A−B)(p−α)]w(z)1+Bw(z), w(z) is analytic in U with w(0)=0 and |w(z)|≦|z| for z∈U. In this paper we obtain the bounds of an and we maximize |ap+2−μap+12| over the class Sλ(A,B,p,α) for complex values of μ

Subordination and superordination of certain linear operator on meromorphic functions

Using the methods of differential subordination and superordination, sufficient conditions are determined on the differential linear operator of meromorphic functions in the punctured unit disk to obtain, respectively, the best dominant and the best subordinant. New sandwich-type results are also obtained

Hankel determinant for a class of analytic functions of complex order defined by convolution

In this paper, we obtain the Fekete-Szego inequalities for the functions of complex order defined by convolution. Also, we find upper bounds for the second Hankel determinant $|a_2a_4-a_3^2|$ for functions belonging to the class $S_{\gamma}^b(g(z);A,B)$

A remark on certain p

The object of the present paper is to prove an interesting result for certain analytic and p-valent functions in the unit disc U={z:|z|<1}

On differential sandwich theorems of analytic functions defined by certain linear operator

In this paper, we obtain some applications of first order differential subordination and superordination results involving certain linear operator and other linear operators for certain normalized analytic functions. Some of our results improve and generalize previously known results

On certain classes of p

Let Vkλ(α,b,p) (k≥2, b≠0 is any complex number, 0≤α<p and |λ|<π/2) denote the class of functions f(z)=zp+∑n=p+1∞anzn analytic in U={z:|z|<1} having (p−1) critical points in U and satisfyinglimr→1−sup∫02π|Re{eiλ[p+1b(1+zf″(z)f′(z)−p)]−αcosλ}p−α|dθ≤kπcosλ.In this paper we generalize both those functions f(z) which are p-valent convex of order α, 0≤α<p, with bounded boundary rotation and those p-valent functions f(z) for which zf′(z)/p is λ-spirallike of order α, 0≤α<p

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

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

Inclusion properties of certain subclasses of analytic functions defined by generalized Salagean operator

Let $A$ denote the class of analytic functions with the normalization $f(0)=f^{\prime }(0)-1=0$ in the open unit disc U=\{z:\left\vert z\right\vert <1\}.  Set $$f_{\lambda }^{n}(z)=z+\sum_{k=2}^{\infty }[1+\lambda (k-1)]^{n}z^{k}\quad(n\in N_{0};\ \lambda \geq 0;\ z\in U),$$ and define $f_{\lambda ,\mu }^{n}$ in terms of the Hadamard product f_{\lambda }^{n}(z)\ast f_{\lambda ,\mu }^{n}=\frac{z}{(1-z)^{\mu }}\quad (\mu >0;\ z\in U). In this paper, we introduce several subclasses of analytic functions defined by means of the operator $I_{\lambda ,\mu }^{n}:A\longrightarrow A$, given by I_{\lambda ,\mu }^{n}f(z)=f_{\lambda ,\mu }^{n}(z)\ast f(z)\quad (f\in A;\ n\in N_{0;}\ \lambda \geq 0;\ \mu >0). Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered

On convolution properties for certain classes of p-valent meromorphic functions defined by linear operator

In this paper, by making use of convolution, we obtain some interesting results for certain family of meromorphic p-valent functions defined by new linear operator.