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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.

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]

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 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.

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]