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In this paper we establish the Lp boundedness of Marcinkiewicz integral operators on product domains with rough kernels satisfying a weak size condition. We assume that our kernels are supported on surfaces generated by curves more general than polynomials and convex functions. This generalizes and extends previous results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate harmonic univalent functions convex in the direction 𝜃, for 𝜃 ∈ [0,π). We find bounds for |fz(z)|, and |f(z)|, as well as coefficient bounds on the series expansion of functions convex in a given direction. [ABSTRACT FROM AUTHOR]

In the present paper, we determine new characterisations of the sub-classes TS*C(α, β, γ) and TCC(; fi;) of analytic functions associated with Pascal distribution series ... mzn. Further, we give necessary and suficient conditions for an integral operator related to Pascal distribution series Gmq f(z) = R z 0 mq (t) t dt to belong to the above classes. Several corollaries and consequences of the main results are also considered. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new classes of post-quantum or (p; q)-starlike and convex functions with respect to symmetric points associated with a cardiod-shaped domain. We obtain (p; q)-Fekete-Szego inequalities for functions in these classes. We also obtain estimates of initial (p; q)-logarithmic coefficients. In addition, we get q-Bieberbachde-Branges type inequalities for the special case of our classes when p = 1. Moreover, we also discuss some special cases of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate an interesting subclass ℳΣ(γλδφ) of analytic and bi-univalent functions of complex order in the open unit disk U. For functions belonging to the class ℳΣ(γλδφ) we investigate the coeffcient estimates on the first two Taylor-Maclaurin coeffcients |a2| and |a3|. The results presented in this paper would generalize and improve some recent works of [1],[5],[9]. [ABSTRACT FROM AUTHOR]

In the present paper, some generalizations of analytic functions have been considered and the bounds of the coefficients of these classes of bi-univalent functions have been investigated. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to investigate Conuent hypergeometric distribution. We obtain some basic properties of this distribution. It is worthy to note that the Poisson distribution is a particular case of this distribution. Finally, we give a nice application of this distribution on certain classes of univalent functions of the conic regions. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to introduce two novel subclasses Tμ(n, λ, α) and Hμ(n, λ, α; κ) of analytic and univalent functions with negative coefficients, involving Ruscheweyh derivative operator. The various results investigated in this paper include coefficient estimates, distortion inequalities, radii of close-to-convexity, star-likenes, and convexity for the functions belonging to the class Tμ (n, λ, α). These results are then appropriately applied to derive similar geometrical properties for the other class Hμ(n, λ, α; κ) of analytic and univalent functions. Relevant connections of these results with those in several earlier investigations are briefly indicated. [ABSTRACT FROM AUTHOR]

In this paper, we obtain Fekete-Szegö inequalities for certain class of meromorphic functions f(z) for which −(1−αq)qzDqf(z)+αqzDq[zDqf(z)](1−αq)f(z)+αzDqf(z)≺φ(z)(α∈C/(0,1], 0

A bounded linear operator T on a Hilbert space H is convex, if for each x ∊ H, ‖T²x‖² -- 2‖Tx‖² + ‖x‖² ≥ 0. In this paper, it is shown that if T is convex and supercyclic then it is a contraction or an expansion. We then present some examples of convex supercyclic operators. Also, it is proved that no convex composition operator induced by an automorphism of the disc on a weighted Hardy space is supercyclic. [ABSTRACT FROM AUTHOR]

In this paper, some Hermite-Hadamard-Fejer type integral inequalities for harmonically quasi-convex functions in fractional integral forms have been obtained. [ABSTRACT FROM AUTHOR]

In this paper, we obtain Fekete-Szegö inequalities for certain subclasses of analytic univalent functions of complex order associated with quasi-subordination. [ABSTRACT FROM AUTHOR]

The objective of this paper is to obtain sharp upper bound for the second []1 Hankel functional associated with the kth root transform f(zk)1/k of normalized analytic function f(z) when it belongs to the class of starlike and convex functions with respect to symmetric points, defined on the open unit disc in the complex plane, using Toeplitz determinants. [ABSTRACT FROM AUTHOR]

In this paper, we define two new subclass of κ-uniformly starlike and convex functions of order α type β with varying argument of coefficients. Further, we obtain coefficient estimates, extreme points, growth and distortion bounds, radii of starlikeness, convexity and results on modified Hadamard products. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to establish some interesting results involving coefficient conditions, extreme points, distortion bounds and covering theorems for the classes VH(β) and UH(β). Further, various inclusion relations are also obtained for these classes. We also discuss a class preserving integral operator and show that these classes are closed under convolution and convex combinations. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to obtain some subordination- and superordination- preserving properties for multivalent function associated the differintegral operators defined on the space of normalized analytic functions in the open unit disk. The sandwich type theorem for the integral operator is also considered. [ABSTRACT FROM AUTHOR]

In this paper, we prove some inequalities in terms of Gâteaux derivatives for convex functions defined on linear spaces and also give improvement of Jensen's inequality. Furthermore, we give applications for norms, mean f-deviations and f-divergence measures. [ABSTRACT FROM AUTHOR]

In this paper we establish several Hadamard-type integral inequalities for (α,m)-convex functions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a comprehensive family of harmonic univalent functions which contains various well-known classes of harmonic univalent functions as well as many new ones. Also, we improve some results obtained by Frasin [3] and obtain coefficient bounds, distortion bounds and extreme points, convolution conditions and convex combination are also determined for functions in this family. It is worth mentioning that many of our results are either extensions or new approaches to those corresponding previously known results. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to introduce a new subclass of meromorphic multivalent functions defined by using a linear operator associated with the generalized hypergeometric function. Some properties of this class are established here by using the principle of differential subordination and convolution in geometric function theory. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce and investigate a new subclass of multivalent functions associated with the Cho-Kwon-Srivastava operator τpλ (a, c). Such results as inclusion relationships, convolution properties and criteria for starlikeness are proved. Relevant connections of the results presented here with those obtained in earlier works are also pointed out. [ABSTRACT FROM AUTHOR]

In the present paper we introduce the subclass Saclambda (p,A,B) of analytic functions and then we investigate some interesting properties of functions belonging to this subclass. Our results generalize many results known in the literature and especially generalize some of the results obtained by Ling and Liu [5]. [ABSTRACT FROM AUTHOR]

In the present paper we shall prove that on a foundation *-semigroup S with an identity and with a locally bounded Borel measurable weight function ω, the pointwise convergence and the uniform convergence of a sequence of ω-bounded exponentially convex functions on S which are also continuous at the identity are equivalent. [ABSTRACT FROM AUTHOR]