PARTIAL SUMS OF GENERALIZED CLASS OF HARMONIC UNIVALENT FUNCTIONS INVOLVING A GAUSSIAN HYPERGEOMETRIC FUNCTION
The purpose of the present paper is to establish some new results giving the sharp bounds of the real parts of ratios of harmonic univalent functions to its sequences of partial sums by involving the Gaussian hypergeometric function. Relevant connections of the results presented here with various known results are briefly indicated. We also mention results which are associated with certain classical orthogonal polynomials (deduced from some of the main results) exhibiting the usefulness of the results presented in this paper.
Convex subclass of harmonic starlike functions
Complex valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f=h+g@?, where h and g are analytic in U. We define and investigate a convex subclass of harmonic starlike functions of order @a (0=<@a<1). We obtain coefficient conditions, extreme points, distortion bounds, convolution conditions, and convex combination for the above class of harmonic functions.
The Role of Nonclassroom Spaces in Living-Learning Communities.
A body of research suggests that learning communities provide a range of academic benefits by increasing social connectedness. Researchers have also hypothesized that informal learning spaces -- nonclassroom spaces (NCSs) -- can facilitate learning by supporting social connectedness. This study uses qualitative methods to explore the way nonclassroom spaces facilitate learning-related activities within a recently established learning community at State University. Our findings suggest that NCSs function as social hubs, help make intellectual and creative work visible to the larger learning community, and provide access to important resources. More generally, NCSs help to facilitate community formation and identity.