Search

Let f be a transcendental meromorphic function of finite order in the plane such that f(m) has finitely many zeros for some positive integer m ≥ 2. Suppose that f(k) and f share a CM, where k ≥ 1 is a positive integer, a≠ 0 is a finite complex value. Then f is an entire function such that f(k) - a = c(f - a), where c≠ 0 is a nonzero constant. The results in this paper are concerning a conjecture of Brück [5]. An example is provided to show that the results in this paper, in a sense, are the best possible. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the uniqueness problem of entire functions sharing two polynomials with their k-th derivatives. We look into the conjecture given by Lü, Li and Yang [Bull. Korean Math. Soc., 51(2014), 1281{1289] for the case F = fnP(f), where f is a transcendental entire function and P(z) = amzm+am-1zm-1+ ... +a1z+a0(...0), m is a nonnegative integer, am, am-1, . . . , a1, a0 are complex constants and obtain a result which improves and generalizes many previous results. We also provide some examples to show that the conditions taken in our result are best possible. [ABSTRACT FROM AUTHOR]

In this paper, we obtain Fekete-Szegö inequalities for certain class of meromorphic functions f(z) for which −(1−αq)qzDqf(z)+αqzDq[zDqf(z)](1−αq)f(z)+αzDqf(z)≺φ(z)(α∈C/(0,1], 0

In this paper, we generalize some earlier well known results by considering polynomials of lacunary type having some zeros at origin and rest of the zeros on or outside the boundary of a prescribed disk. [ABSTRACT FROM AUTHOR]

Posner's first theorem states that if R is a prime ring of characteristic different from two, d1 and d2 are derivations on R such that the iterate d1d2 is also a derivation of R, then at least one of d1, d2 is zero. In the present paper we extend this result to *-prime rings of characteristic different from two. [ABSTRACT FROM AUTHOR]

A two-direction multiscaling function φ satisfies a recursion relation that uses scaled and translated versions of both itself and its reverse. This offers a more general and flexible setting than standard one-direction wavelet theory. In this paper, we investigate how to find and normalize point values and derivative values of two-direction multiscaling and multiwavelet functions. Determination of point values is based on the eigenvalue approach. Normalization is based on normalizing conditions for the continuous moments of φ. Examples for illustrating the general theory are given. [ABSTRACT FROM AUTHOR]

In the paper we discuss the value distribution of the product of the derivative of a transcendental meromorphic function and a power of the function. [ABSTRACT FROM AUTHOR]

In this paper we derive some results for certain new class of analytic functions defined by using Ruscheweyh derivative with varying arguments. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the commutativity of a semiprime ring R admitting a generalized derivation F with associated derivation D satisfying any one of the properties: (i) F(x)D(y) = [x; y], (ii) D(x)F(y) = F[x; y], (iii) D(x)F(y) = xy, (iv) F(x?y) = [F(x); y] + [D(y); x], and (v) F[x; y] = F(x)?y - D(y)?x for all x; y in some appropriate subsets of R. [ABSTRACT FROM AUTHOR]

In this paper, we prove some inequalities in terms of Gâteaux derivatives for convex functions defined on linear spaces and also give improvement of Jensen's inequality. Furthermore, we give applications for norms, mean f-deviations and f-divergence measures. [ABSTRACT FROM AUTHOR]