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Let H(D) be the set of all analytic functions on the open unit disk D of C, u є H(D) and Φ an entire function on C. In this paper, we characterize the boundedness and compactness of the weighted differentiation superposition operator Dum SΦ from H∞ to the nth weighted-type space. [ABSTRACT FROM AUTHOR]

The main objective of the present paper is to obtain sufficient conditions for the univalence, starlikeness and convexity of a new integral operator defined on the space of normalized analytic functions in the open unit disk. Results presented in this paper may motivate further reserch in this fascinating field. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to investigate some argument properties for certain analytic functions in the open unit disk. The main results presented in here generalize some previous those concerning starlike function of reciprocal of order beta and strongly starlike functions. [ABSTRACT FROM AUTHOR]

In this paper, the authors investigate the [p, q]-order and [p, q]-type of f1+f2, f1f2, f1/f2, where f1, f2 are meromorphic functions or analytic functions with the same [p, q]-order and different [p, q]-type in the unit disc, and the authors also study the [p, q]-order and [p, q]-type of f and its derivative. At the end, the authors investigate the relationship between two different [p, q]-convergence exponents of f. The obtained results are the improvements and supplements to many previous results. [ABSTRACT FROM AUTHOR]

In this paper, we define some general classes of weighted analytic function spaces in the unit disc. For the new classes, we investigate boundedness and compactness of the weighted composition operator uCø under some mild conditions on the weighted functions of the classes. [ABSTRACT FROM AUTHOR]

In this paper, we solve the inhomogeneous Gauss differential equation and apply this result to estimate the error bound occurring when an analytic function is approximated by an appropriate hypergeometric function. [ABSTRACT FROM AUTHOR]

In this paper we introduce an argument property which gives an interesting relation between the classes of strongly convex and strongly starlike functions of order α and type β in the open unit disk. Also, the sufficient condition of starlikeness under cer-tain restrictions is obtained. [ABSTRACT FROM AUTHOR]

In the present paper, we define and investigate a new class of multivalent harmonic functions in the open unit disc U = {z G C : |z| < 1}, under certain conditions involving a new generalized differential operator. Coefficient inequalities, distortion bounds and a covering result are also obtained. [ABSTRACT FROM AUTHOR]

In this present paper, we introduce the new subclass of analytic univalent functions associated with quasi-subordination in the field of sigmoid functions. We obtained the coefficient bounds and Fekete-Szego inequality belongs to the defined class. Also, we extracted the new subclasses from the dened class of analytic functions. [ABSTRACT FROM AUTHOR]

In this paper, we derive some bounds for the real parts and arguments of the functionals given by ... where Js;b is the widely-investigated Srivastava-Attiya operator defined on the class of normalized analytic functions f in the open unit disk ... with suitable real parameters s and b. These results reduce upon specialization to some well-known inclusion relationships for several classes of functions with given geometric properties. We also make a comparison between one of the results obtained here and an already known result for some specific cases. [ABSTRACT FROM AUTHOR]

In this paper we consider analytic functions in the unit disc D such that |f(p)(z)| is bounded in D. We present several sufficient conditions for function to be p-valent starlike, convex or strongly starlike of a certain order. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of analytic functions associated with Mittag-Leffler fuction in the open unit disk. Several properties of functions belonging to this class are derived. [ABSTRACT FROM AUTHOR]

Problem statement: We introduce and study a general integral operator defined on the class of normalized analytic functions in the open unit disk. This operator is motivated by many researchers. With this operator univalence conditions for the normalized analytic function in the open unit disk are obtained. In deed, the preserving properties of this class are studied, when the integral operator is applied and we present a few conditions of univalency for our integral operator. The operator is essential to obtain univalence of a certain general integral operator. Approach: In this paper we discuss some extensions of univalent conditions for an integral operator defined by our generalized differential operator. Several other results are also considered. We will prove in this paper the univalent conditions for this integral operator on the class of normalized analytic functions when we make some restrictions about the functions from definitions. Results: Having the integral operator, some interesting properties of this class of functions will be obtained. Relevant connections of the results, shall be presented in the paper. In fact, various other known results are also pointed out. We also and some interesting corollaries on the class of normalized analytic functions in the open unit disk. Conclusion: Therefore, many interesting results could be obtained and we also derive some interesting properties of these classes. We conclude this study with some suggestions for future research, one direction is to study other classes of analytic functions involving our integral operator on the class of normalized analytic functions in the open unit disk. [ABSTRACT FROM AUTHOR]

In this paper we have introduced and studied the subclass L(λ, d, α, β) using the fractional integral as- sociated with the convolution product of Sălăgean operator and Ruscheweyh derivative. The main object is to investigate several properties such as coefficient estimates, distortion theorems, closure theorems, neigh- borhoods and the radii of starlikeness, convexity and close-to-convexity of functions belonging to the class L(λ, d, α, β). [ABSTRACT FROM AUTHOR]

Let A be the class of analytic functions in the open unit disc U with normalization ƒ(0) = ƒ'0 (0) - 1 = 0: The purpose of the present paper is to obtain several sufficient conditions of starlikeness and strongly starlikeness for some subclasses of A with fixed second coefficients that satisfy certain conditions for the quotient of the representations of convexity and starlikeness. [ABSTRACT FROM AUTHOR]

One purpose of this paper is to investigate the growth of analytic function represented by Laplace-Stieltjes transform which is of infinite order and converges in the half plane, and a necessary and sufficient conditions on the growth of Laplace-Stieltjes transforms of finite XU-order was obtained. Besiders, we further investigate the error in approximating on Laplace-Stieltjes transform of finite XU-order, and obtained some relations between the error and growth of Laplace-Stieltjes transforms of finite XU-order. [ABSTRACT FROM AUTHOR]

Let Φ be an analytic self-map of unit disk D, H(D) the space of analytic functions on D, and g ξ H(D). For an analytic function... The boundedness and compactness of C[β] Φ,g from mixed-norm spaces H(p, q, µ) to Bloch-type spaces B! are discussed in this paper. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce and investigate two new subclasses of the function class Σ of bi-univalent functions of complex order defined in the open unit disk, which are associated with the one of the orthogonal polynomial namely Generalized Meixner-Pollaczek polynomials, and satisfying subordinate conditions. Taylor-MacLaurin coefficients |α2| and |α3| were estimated for functions in new subclass. Furthermore, several known consequences are also investigated. [ABSTRACT FROM AUTHOR]

In this paper we derive the famous Fekete-Szegö inequality for the class of p-valent non-bazilevič function using differential operator. [ABSTRACT FROM AUTHOR]

The object of the present paper is to obtain subordination, superordination and sandwich-type results related to a certain family of integral operators defined on the space of multivalent functions in the open unit disk. Also we point out relevant connections of the results presented here with those obtained in earlier. [ABSTRACT FROM AUTHOR]

In this paper we study certain strong differential superordinations, obtained by using a new integral operator introduced in [13]. [ABSTRACT FROM AUTHOR]

The purpose of the presented paper is to derive several properties and characteristics of analytic functions, by applying the differential subordination techniques. Several consequences of the results stated here are also pointed out. [ABSTRACT FROM AUTHOR]

The main object of this paper is to introduce the majorization properties for certain families of analytic functions associated with generalized Srivastava-Attiya operator in the unit disk. Also, some applications of our results are discussed which give a number of new results. [ABSTRACT FROM AUTHOR]

In this work we study a new operator IRm,nλ,l defined as the Hadamard product of the multiplier transformation I (m, λ, l) and Ruscheweyh derivative Rn, given by IRm,n λ,l : A → A, IRm,n λ,l f (z) = (I (m, λ, l) * Rn) f (z) and An = {f ∊ H(U) : f (z) = z + an+1zn+1 + ..., z ∊ U} is the class of normalized analytic functions with A1 = A. The purpose of this paper is to derive certain subordination and superordination results involving the operator IRm,n λ,l and we establish differential sandwich-type theorems. [ABSTRACT FROM AUTHOR]

In this paper we establish some fuzzy differential subordinations regarding the differential operator RIα m,λ;l : An → An, RIαm,λ,lf(z) = (1 - α)Rmf(z) + αI (m, λ, l) f(z); where Rm is the Ruscheweyh derivative,I (m, λ; l) is the multiplier transformation and An = {f ∊ H(U), f(z) = z +an + 1zn+1 +... , z ∊ U} is the class of normalized analytic functions. We introduce a fuzzy class RIδF (α, m; λ, l) and by using the fuzzy differential subordinations we derive some properties of this class: Also, several fuzzy differential subordinations are established regarding the studied differential operator. [ABSTRACT FROM AUTHOR]

For functions belonging to the class Sm (δ, α), δ ϵ [0, 1), α ≥ 0 and in ϵ N, of normalized analytic functions in the open unit disc U, which are investigated in this paper, the author derives several interesting differential subordination results. These subordinations are established by means of a special case of the multiplier transformations Ip (m, λ, l) ƒ(z) namely >>>>>Ip (m, λ, l) ƒ(z) ≔ zp + Σj=p+n∞ (p + λ(j - 1) + l/p + 1)m ajzj, where p, n ϵ N, m ϵ NU {0}, λ, l ≥ 0 and ƒ ϵ A(p,n), A (p,n) = {ƒ ϵ H(U) : ƒ(z) = zp + Σj=p+n∞ ajzj, z ϵ U). A number of interesting consequences of some of these subordination results are discussed. Relevant connections of some of the new results obtained in this paper with those in earlier works are also provided. [ABSTRACT FROM AUTHOR]

In the present paper we have characterised (α, β) — LP orthogonality in a 2-normed linear space. In some way the results proved in this paper generalize some of the similar characterization of generalized LP- orthogonality derived earlier by Zheng Liu[8]. [ABSTRACT FROM AUTHOR]

In this paper, we have established the inclusion relations for k-uniformly starlike functions under the (Dqf)(z) operator. We define two new sub-class of k-uniformly starlike functions of order α. Moreover, for functions belonging to these function classes, we investigate necessary and suffcient coeffcient conditions, distortion bounds, extreme points. [ABSTRACT FROM AUTHOR]

In this paper, we study the zeros of functions in weighted Dirichlet space and a class of Carleson type measure. [ABSTRACT FROM AUTHOR]

This paper introduces new subclasses of analytic functions and investigate the inclusion properties of these subclasses using the generalized Bessel functions of the first kind. We also derive a variety of special cases and corollaries of the main results. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce and investigate a new subclass of bi-univalent functions of complex order defined in the open unit disk, which are associated with Wright hypergeometric functions and satisfying quasi-subordinate conditions. Furthermore, we find estimates on the second and the third coefficients of the Taylor-Maclaurin series for functions in the new subclass. Several special consequences of the results are also pointed out. [ABSTRACT FROM AUTHOR]

In this paper we obtain some subordination and superordination results for the operator IRλ.lm,n and we establish di erential sandwich-type theorems. The operator IRλ.lm,n is defined as the Hadamard product of the multiplier transformation I (m, λ l) and Ruscheweyh derivative Rn. [ABSTRACT FROM AUTHOR]

In this paper we introduce a class of complex Stancu type summation- integral operators and study the approximation properties of these operators. We obtain a Voronovskaja-type result with quantitative estimate for these oper- ators attached to analytic functions on compact disks. We also study the exact order of approximation. More important, our results show the overconvergence phenomenon for these complex operators. [ABSTRACT FROM AUTHOR]

In this paper we characterize the boundedness and compactness of the weighted composition operator from the classical Bloch space β to the Zygmund space Z, and from the little Bloch space β0 to the little Zygmund space Z0, respectively. [ABSTRACT FROM AUTHOR]

In the present paper we establish several fuzzy differential subordinations regardind the operator I (m; λ; l), given by I (m; λ; l) : A → A, I (m; λ; l) f (z) = z +Σ∞j=2 (1+λ(j-1)+l/ l+1)m ajzj and A = {f ∊ H(U); f(z) =z + a2z2 +...., ∊ 2 Ug is the class of normalized analytic functions. A certain fuzzy class, denoted by SIδF (m; λ; l) ; of analytic functions in the open unit disc is introduced by means of this operator. By making use of the concept of fuzzy differential subordination we will derive various properties and characteristics of the class SIδ F (m; λ; l) : Also, several fuzzy differential subordinations are established regarding the operator I (m; λ; l). [ABSTRACT FROM AUTHOR]

In this paper, we are interested in the isometric equivalence problem for the weighted composition operator Wu,φ and the composition operator Cφ on the Hardy and the Dirichlet space. We show what properties the operators must satisfy to insure that they are isometric equivalent. [ABSTRACT FROM AUTHOR]

Let φ denote a nonconstant analytic self-map of the open unit disk D, g be an analytic function on D. In this paper, we characterize the necessary or sufficient conditions for generalized composition operators Cgφ f(z) = ∫ z 0 f'(φ(ξ))g(ξ)dξ, on the Bloch-type spaces to have a closed range. Moreover, if g ∊ H∞, according to relationship betweenα and β, we show several conclusions. [ABSTRACT FROM AUTHOR]

In this paper, we first investigate and present several sets of sufficient conditions for Carathéodory functions in the open unit disk U. We then apply the main results proven here in order to derive some conditions for starlike functions in U. Relevant connections with various known results are also considered. [ABSTRACT FROM AUTHOR]

this paper we have introduced and studied the subclass L(d, α, β) of univalent functions defined by the linear operator Lnʏ f(z) defined by using the Ruscheweyh derivative Rnf(z) and the Să lăgean operator Snf(z), as Lnʏ : A → A, Lnʏ f(z) = (1- ʏ)Rnf(z)+ʏSnf(z), z ϵ U, where An = {f ϵ H(U) : f(z) = z+an+1zn+1 + . . . , z ϵ U} is the class of normalized analytic functions with A1 = A. The main object is to investigate several properties such as coefficient estimates, distortion theorems, closure theorems, neighborhoods and the radii of starlikeness, convexity and close-to-convexity of functions belonging to the class L(d, α, β). [ABSTRACT FROM AUTHOR]

In this work we study a new operator IRm,n λ,l defined as the Hadamard product of the multiplier transformation I (m, λ, l) and Ruscheweyh derivative Rn, given by IRm,n λ,l : A → A, IRm,n λ,l f (z) = (I (m, λ, l) * Rn) f (z) and An = {f ϵ H(U) : f (z) = z +an+1zn+1 +..., z ϵ U} is the class of normalized analytic functions with A1 = A. The purpose of this paper is to derive certain subordination and superordination results involving the operator IRm,n λ.l and we establish differential sandwich-type theorems. [ABSTRACT FROM AUTHOR]

In this paper, we characterize the essential commutativity and isometry of composition operator and differentiation operator from the Bloch type space to space of all weighted bounded analytic functions in the disk. [ABSTRACT FROM AUTHOR]

In this paper we use the differential subordinations techniques to obtain some properties of functions belonging to the class of analytic functions in the open unit disc U. Also, some properties of the class of two fixed points in U; are also discussed. Furthermore, some interesting results of Hurwitz Lerch Zeta function and Digamma function are obtained. [ABSTRACT FROM AUTHOR]

In this paper we introduce a kind of complex summation-integral type operators and study the approximation properties of these operators. We obtain a Voronovskaja-type result with quantitative estimate for these operators attached to analytic functions on compact disks. We also study the exact order of approximation. More important, our results show the overconvergence phenomenon for these complex operators. [ABSTRACT FROM AUTHOR]

In this paper, the order of simultaneous approximation and Voronovskaya type theorems with quantitative estimate for complex q-Gamma operators attached to analytic functions in compact disks are obtained. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to investigate some characterization for generalized Bessel functions of first kind to be in the new subclasses G(λ, α) and K(λ, α) of analytic functions. [ABSTRACT FROM AUTHOR]

In this paper we define some new integral operators on classes of analytic functions and we study certain differential subordinations obtained by using those operators. [ABSTRACT FROM AUTHOR]

In this paper we introduce new classes containig the linear operator RIn, λ, lα : A → A, RIn, λ, lα f(z) = (1 - α)Rnf(z) + αI (n, λ, l) f(z), ∈ U, where Rnf(z) is the Ruscheweyh derivative, I (n, λ, l) f(z) the multiplier transformation and An = {f ∈ H(U) : f(z) = z + an+1zn+1 + ..., z ∈ U} is the class of normalized analytic functions with A1 = A. Characterization and other properties of these classes are studied. [ABSTRACT FROM AUTHOR]

The main object of this paper is to study some properties of certain subclass of analytic functions in the open unit disc which is defined by the linear operator Lαn : A → A, Lαnf(z) = (1 - α)Rnf(z) + αSnf(z), z ∈ U, where Rnf(z) is the Ruscheweyh derivative, Snf(z) the Sălăgean operator and An = {f ∈ H(U) : f(z) = z + an+1zn+1 + ..., z ∈ U} is the class of normalized analytic functions with A1 = A. These properties include a coefficient inequality, distorsion theorem and extreme points of differential operator. We also discuss the boundedness properties associated with partial sums of functions in the class TSαn (β, γ) . [ABSTRACT FROM AUTHOR]

In the present paper, we obtain coefficient inequalities, inclusion relationships involving neighborhoods, subordination results, properties involving modified Hadamard products and also study majorization properties of certain subclasses of multivalent analytic functions, which are defined by means of a certain linear operator. Some useful consequences our main results are mentioned and their relevance with some of the earlier results are also pointed out. [ABSTRACT FROM AUTHOR]

In this work we define a new operator using the generalized Sălăgean operator and Ruscheweyh operator. Denote by DRm, nλ the Hadamard product of the generalized Sălăgean operator DRmλ and Ruscheweyh operator Rn, given by DRm, nλ: A→A, DRm, nλf(z) = DRmλ * Rnf(z) and An = {f ∈ H(U) : f(z) z +an+1zn+1 + ..., z ∈ U} is the class of normalized analytic functions with A1 = A. The purpose of this paper is to introduce sufficient conditions for subordination and superordination involving the operator DRm, nλ and also to obtain sandwich-type results. [ABSTRACT FROM AUTHOR]