The Wright’s generalized hypergeometric function is used here to introduce a new class of p-valent functions WT p(λ, α, β) defined in the open unit disc and investigate its various characteristics. Further we obtain distortion bounds, extreme points and radii of close-to-convexity, starlikeness and convexity of functions belonging to the class WT p(λ, α, β).

in this article, we consider the uniqueness of the difference monomials $f^{n}(z)f(z+c)$. suppose that $f(z)$ and $g(z)$ are transcendental meromorphic functions with finite order and $e_k(1, f^{n}(z)f(z+c))=e_k(1, g^{n}(z)g(z+c))$. then we prove that if one of the following holds (i) $n geq 14$ and $kgeq 3$, (ii) $n geq 16$ and $k=2$, (iii) $n geq 22$ and $k=1$, then $f(z)equiv t_1g(z)$ or $f(...

In this paper, we obtain some sufficient conditions for general p−valent integral operators to be the p−th power of a univalent functions in the open unit disk.

A rigid meromorphic cocycle is a class in the first cohomology of the discrete group Γ := SL2(Z[1/p]) with values in the multiplicative group of non-zero rigid meromorphic functions on the p-adic upper half planeHp := P1(Cp)−P1(Qp). Such a class can be evaluated at the real quadratic irrationalities in Hp, which are referred to as “RM points”. The RM values of arbitrary rigid meromorphic cocycl...

In this paper, we investigate the growth of meromorphic solutions to a complex higher order linear differential equation whose coefficients are meromorphic functions of [p, q]-orders. We get the results about the lower [p, q]-order of solutions of the equation. Moreover, we investigate the [p, q]-convergence exponent and the lower [p, q]-convergence exponent of distinct zeros of f(z)− φ(z). AMS...

We introduce two subclasses T ∗(p, α, j) and C(p, α, j) (0 ≤ α < p − j + 1, 1 ≤ j ≤ p, p ∈ N = {1, 2, . . .}) of p-valent starlike and p-valent convex functions with negative coefficents. In this paper we obtain coefficient inequalities, distortion theorems, extreme points and integral operators for functions belonging to the classes T ∗(p, α, j) and C(p, α, j). We also determine the radii of c...