In this paper, we consider a new class of analytic functions in the unit disk using polynomials of order alpha. We give some sufficient conditions for functions belonging to this class.

It is well known that an entire function of finite order has an at most countable number of asymptotic values. Gross [I] constructed an example of an entire function of infinite order whose set of asymptotic values coincides with the extended complex plane. Dreisin and Weizmann [2] raised the question of whether there are any restrictions from above on the size of the set of asymptotic values o...

We prove a unicity theorem of Nevanlinna for meromorphic mappings of P into Pm. 1. INTR~DuOTI~N As an application of Nevanlinna’s second main theorem and Borel’s lemma, R. Nevanlinna proved that for any two meromorphic functions in the complex plane @ on which they share four distinct values, then, these two meromorphic functions are the same up to a Mijbius transformation. Since then, there ha...

In an earlier paper [l] the writer showed the development of a variational method for starlike functions and applied this method to a general class of extremal problems connected with the coefficients of the function. It is the purpose of this paper to study the classes of extremal problems to which this variational method can be applied and to make some remarks as to its utility. The class S* ...

ABSTRACT. The second fundamental theorem of Nevanlinna concerning meromorphic functions of a complex variable is extended in this note to an analogous result for meromorphic minimal surfaces. A similar extension of the first fundamental theorem involved generalizations of the classical proximity and enumerative functions and also a new visibility function; for the present result, a second enume...

Abstract Keeping in view the latest trends toward quantum calculus, due to its various applications physics and applied mathematics, we introduce a new subclass of meromorphic multivalent functions Janowski domain with help q -differential operator. Furthermore, investigate some useful geometric algebraic properties these functions. We discuss sufficiency criteria, distortion bounds, coefficien...

The aim of the present paper is to study the relations between the prime distribution and the zero distribution for generalized zeta functions which are expressed by an Euler products and are analytically continued as meromorphic functions of finite order. In this paper, we give an inequality between the order of the zeta function as a meromorphic function and the growth of the multiplicity in ...

We determine the sufficient conditions for function f(z) = z + a2z2 ... to be starlike of order 1/2, which shows also starlikeness f.

We extend the “Extension after Restriction Principle” for symplectic embeddings of bounded starlike domains to a large class of symplectic embeddings of unbounded starlike domains.

In this work, we examine the stationary one-dimensional classical Poisson-Nernst-Planck (cPNP) model for ionic flow – a singularly perturbed boundary value problem (BVP). For the case of zero permanent charge, we provide a complete answer concerning the existence and uniqueness of the BVP. The analysis relies on a number of ingredients: a geometric singular perturbation framework for a reductio...