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Using the third-order differential subordination basic results, we introduce certain classes of admissible functions and investigate some applications of third-order differential subordination for p-valent functions associated with generalized fractional differintegral operator.

By making use of the pre-Schwarzian norm given bywe obtain such norm estimates for Hohlov operator of functions belonging to the class of uniformly convex functions of orderαand typeβ. We also employ an entirely new method to generalize and extend the results of Theorems 1, 2 and 3 in [3]. Finally, some inequalities concerning the norm of the pre-Schwarzian derivative for Dziok-Srivastava operator are also considered.

The main object of this paper is to investigate some subordination results of certain subclasses of multivalent analytic functions which are defined by a generalized fractional differintegral operator. Inclusion relations for functions in the class $\mathcal {S}_{p,q}^{\lambda,\mu,\eta }\left (\zeta ;A,B\right) \ $ and the images of these functions by the generalized Bernardi-Libera-Livingston integral operator are also considered.

We introduce sufficient conditions for (Gaussian) hypergeometric functions to be in a subclass of analytic functions. In addition, we investigate several mapping properties for convolutions and integral convolutions involving hypergeometric functions.

By making use of the q-derivative operator in conjunction with the principle of subordination between analytic functions, we introduce two subclasses of analytic functions in the open unit disk U. We investigate convolution properties and coefficient estimates for these subclasses.

In this paper, we obtain Fekete-Szegö functional |a₁-μa₀²| for functions of the classes Σ_{q}^{∗}(ϕ) and Σ_{q,λ,b}^{∗}(g,ϕ) using quasi-subordination. Sharp bounds for the Fekete-Szegö functional |a₁-μa₀²| are obtained. Also, applications of the main results for subclasses of functions defined by Bessel function are also considered.

In the literature on geometric function theory, we can nd many interesting applications of a variety of convolutionoperators which are de ned by means of a number of special functions and analytic number theory. The main object ofthis paper is to examine two subclasses of multivalent functions of the form f(z) = zp +1X k=p+1akzk;which are analytic in the open unit disc U. We investigate convolution properties and coe cient estimates for thesesubclasses.

In this paper, by making use of the principle of subordination, we investigate some subordination and convolution properties of certain subclasses of $$\ p$$ -valent analytic functions which are defined by the Srivastava–Saigo–Owa fractional differintegral operator.

In this paper we introduce and study the class$\ \mathcal{VR}_{\delta ,\eta }(n,\lambda ,\alpha )\ $of analytic functions with varying arguments of coefficients. We obtain coefficients inequalities, distortion theorems involving fractional calculus, radii of close to convexity, starlikeness and convexity and square root transformation for functions in the class $% \mathcal{VR}_{\delta ,\eta }(n,\lambda ,\alpha )$.\ Finally, integral convolution for functions in this class are considered.

The purpose of this paper is to introduce subclasses of multivalent functions by using Srivastava–Saigo–Owa fractional differintegral operator and investigate various properties for these subclasses. Also, we investigate inclusion relations involving the operator $$F_{p,c}$$ .

In this paper, we obtain subordination, superordination and sandwich-type results regarding to certain family of integral operators defined on the space of multivalent functions in the open unit disk. Also, an application of the subordination and superordination theorems to the Gauss hypergeometric function are considered. These new results generalize some previously well-known sandwich-type theorems.

The purpose of the present paper is to investigate some subordination and other properties of several subclasses of multivalent functions which are defined by the Srivastava–Saigo–Owa fractional differintegral operator. Inclusion relations for functions in the class $$\mathcal {S}_{p,\lambda ,\mu ,\eta }^{m,\delta ,\zeta }(\alpha; A, B)$$ and the images of these functions by the generalized Bernardi–Libera–Livingston integral operator are also considered.

Making use of the operator L q , ν associated with functions of the form f ( z ) = 1 z + ∑ k = 1 ∞ a k z k − 1 , which are analytic in the punctured unit disc U * : = U ∖ { 0 } , we introduce two subclasses of meromorphic functions and investigate convolution properties and coefficient estimates for these subclasses.

In this paper we obtain subordination, superordination, and sandwich-type results related to certain family of integral operators defined on the space of meromorphic functions in the open unit disk. Also, an application of the subordination and superordination theorems to the Gauss hypergeometric function are considered, and the main new results generalize some previously well-known sandwich-type theorems.

The purpose of this paper is to introduce new integral operators associated with Srivastava–Saigo–Owa fractional differintegral operator. We investigate some properties for the integral operators \({\mathcal {F}}_{p,\eta ,\mu }^{\lambda ,\delta }(z)\) and \({\mathcal {G}}_{p,\eta ,\mu }^{\lambda ,\delta }(z)\) to be in the classes \({\mathcal {R}}_{k}^{\zeta }\left( p,\rho \right) \) and \({\mathcal {V}}_{k}^{\zeta }\left( p,\rho \right) \).

The purpose of this paper is to introduce sufficient conditions for (Gaussian) hypergeometric functions to be in various subclasses of analytic functions. Also, we investigate several mapping properties involving these subclasses.

Using of the principle of subordination, we investigate some subordination and convolution properties for classes of multivalent functions under certain assumptions on the parameters involved, which are defined by a generalized fractional differintegral operator under certain assumptions on the parameters involved.

The purpose of this paper is to introduce two subclasses of meromorphic functions by using Cho-Kwon-Srivastava operator and to investigate various characterizations for these subclasses.

In this paper, we obtain Fekete–Szego inequalities for a certain class of meromorphic functions f(z) for which - zf ′ ( z ) + α z 2 f ″ ( z ) ( 1 - α ) f ( z ) + α zf ′ ( z ) ≺ φ ( z ) ( α ∈ C - ( 0 , 1 ] ) . Sharp bounds for the Fekete–Szego functional a 1 - μ a 0 2 are obtained.

For a generalized fractional differintegral operator associated with p -valent functions, we study different properties of differential subordination and superordination related to this operator. Keywords: Analytic, p -valent functions, differential subordination and superordination, generalized fractional derivative operator, generalized fractional integral operator