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.
Quasi Partial Sums of Harmonic Univalent Functions
In this work, we obtain some conditions under which the quasi partial sums of the generalized Bernardi integral operator consisting of the harmonic univalent functions belongs to a similar class.
Do Potential People Have Moral Rights?
By a potential person I shall mean an entity which is not now a person but which is capable of developing into a person, given certain biologically and/or technologically possible conditions. This is admittedly a narrower sense than some would attach to the term ‘potential'. After all, people of the twenty-fifth century, if such there will be, are in some sense potential people now, even though the specific biological entities from which they will develop, i.e. the particular gametes or concepti, do not yet exist. For there do exist, in the reproductive capacities of people now living and in the earth's resources, conditions adequate to produce these future people eventually, provided of course that various possible catastrophes are avoided. Indeed, in some sense of ‘potential’ there have been countless billions of potential people from the beginning of time. But I am concerned not with such remote potentialities but with currently existing entities that are capable of developing into people.