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We study a family of harmonic univalent functions in the open unit disc defined by using post quantum calculus operators. We first obtained a coefficient characterization of these functions. Using this, coefficients estimates, distortion and covering theorems were also obtained. The extreme points of the family and a radius result were also obtained. The results obtained include several known results as special cases.

We introduce three classes of analytic functions with fixed second coefficients that are defined using the class P of analytic functions with positive real parts. The objective of this paper is to determine the radii such that the three classes are contained in various subclasses of starlike functions. The radii estimated in the present investigation are better than the radii obtained earlier. Furthermore, connections with previously known results are shown. [ABSTRACT FROM AUTHOR]

We introduce a new subclass of Sălăgean-type harmonic multivalent functions by using q--difference operator. We investigate sufficient coefficient estimates, distortion bounds, extreme points, convolution properties and neighborhood for the functions belonging to this function class. [ABSTRACT FROM AUTHOR]

For λ ≥ 0, p > 0 and a normalized univalent function f defined on the unit disk D, we consider the harmonic function defined by Tλ,p[f](z) = Dλf(z) + pz(Dλf(z))'/p + 1 + Dλf(z) - pz(Dλf(z))'/p + 1 ; z ∊ D; where the operator Dλ is the familiar λ-Ruscheweyh derivative operator. We find some necessary and sufficient conditions for the univalence, starlikeness and convex- ity as well as the growth estimate of the function Tλ;p[f]. An extension of the above operator is also given. [ABSTRACT FROM AUTHOR]

In this paper, we investigate q- analogues of Bieberbach- de Branges theorems and Fekete-Szegö inequalities for certain families of q- convex and q- close-to-convex functions. [ABSTRACT FROM AUTHOR]

Several inclusions between the class of functions with positive real part and the class of starlike univalent functions associated with lemniscate of Bernoulli are obtained by making use of the well-known theory of differential subordination. Further, these inclusions give suficient conditions for normalized analytic functions to belong to some subclasses of starlike functions. The results also provide sharp version of some previously known results. [ABSTRACT FROM AUTHOR]

The convolution of harmonic functions, unlike the analytic case, proved to be very challenging. In this paper, we introduce dilatation conditions that guarantee the convolution of two harmonic functions to be locally one-to-one, sense-preserving, and close-to-convex harmonic in the unit disk. [ABSTRACT FROM AUTHOR]

In the present investigation we solve Fekete-Szegö problem for the generalized linear differential operator. In particular, our theorems contain corresponding results for various subclasses of strongly starlike and strongly convex functions [ABSTRACT FROM AUTHOR]

For an analytic univalent function f(z) = z + ... αnzn in the unit disk, it is well-known that |an| ≤ n for n ≥ 2. But the inequality |an| ≤ n does not imply the univalence of f. This motivated several authors to determine various radii constants associated with the analytic functions having prescribed coefficient bounds. In this paper, a survey of the related work is presented for analytic and harmonic mappings. In addition, we establish a coefficient inequality for sense-preserving harmonic functions to compute the bounds for the radius of univalence, radius of full starlikeness/convexity of order α (0 ≤ α < 1) for functions with prescribed coefficient bound on the analytic part. [ABSTRACT FROM AUTHOR]

In this paper we use shear construction to generate certain subclasses of harmonic univalent mappings with directional convexity because it allows us to study such functions by examining their related conformal univalent mappings. In this setting we find growth, distortion, and coefficient bounds for harmonic univalent mappings that are convex in both the directions of real axis and imaginary axis. [ABSTRACT FROM AUTHOR]

The object of this article is to study harmonic starlikeness and harmonic convexity of integral operators generated by hypergeometeric series. We also consider special cases of harmonic starlikeness and convexity of integral operators generated by incomplete beta functions. [ABSTRACT FROM AUTHOR]

The article discusses the relationship of neighborhoods of starlike and convex functions with parabola. It mentions several mathematicians who introduced additional general notions of neighbourhood of an analytic function. It states that problems related to the neighbourhoods of analytic functions were given consideration and examples are shown through mathematical notation and formulas. The result of the investigation of the geometric properties are also presented through a series of computations.

Let SH be the family of all planar harmonic, univalent and sense-preserving mappings f=h+g¯ where h and g are analytic funtions in the open unit disk. The purpose of this article is to investigate connections between the theory of harmonic mappings in the plane and hypergeometric functions by applying certain planar harmonic convolution operators on various subclasses of SH. [ABSTRACT FROM AUTHOR]

In September 1989, the United States' Governors Conference in Charlottesville, Virginia set an ambitious goal by declaring that "By the year 2000, United States students will be first in the world in mathematics and science achievements". However, recent results of the 'Programme for International Student Achievement' and 'Trends in International Mathematics and Science Study' indicate that the United States students' achievements in mathematics are far below world class standards. This paper seeks to discuss issues in an international context related to the goal of creating world-class high quality mathematics education for all K-12 American students. In particular, the author also shares his reflections and depicts lessons from Singapore's success story in mathematics education. [ABSTRACT FROM AUTHOR]

Abstract: Inequalities involving multipliers using the sequences and of positive real numbers are introduced for complex-valued harmonic univalent functions. By specializing and , we determine representation theorems, distortion bounds, convolutions, convex combinations, and neighbourhoods for such functions. The theorems presented, in many cases, confirm or generalize various well-known results for corresponding classes of harmonic functions. [Copyright &y& Elsevier]