Related papers: Uniqueness of Meromorphic functions concerning k-t…
We consider transcendental meromorphic functions for which the zeros, 1-points and poles are distributed on three distinct rays. We show that such functions exist if and only if the rays are equally spaced. We also obtain a normal family…
The Riemann-Liouville formula for fractional derivatives and integrals (differintegration) is used to derive formulae for matrix order derivatives and integrals. That is, the parameter for integration and differentiation is allowed to…
This paper studies the uniqueness of two non-integral finite ordered meromorphic functions with finitely many poles when they share two finite sets. Also, studies an answer to a question posed by Gross for a particular class of meromorphic…
n this article we consider functions meromorphic in the unit disk. We give an elementary proof for a condition that is sufficient for the univalence of such functions which also contains some known results. We include few open problems for…
In this document I recapitulate some results by Hiriart-Urruty and Ye (1995) concerning the properties of differentiability and the existence of lateral directional derivatives of the multiple eigenvalues of a complex Hermitian matrix…
We establish pointwise growth estimates for the spherical derivative of solutions of the first order algebraic differential equations. A generalization of this result to higher order equations is also given. We discuss the related question…
The main result of the paper determines all real meromorphic functions of finite order in the plane for which the first derivative has finitely many zeros, while the function itself and one of its higher derivatives have finitely many…
We obtain a family of functional identities satisfied by vector-valued functions of two variables and their geometric inversions. For this we introduce particular differential operators of arbitrary order attached to Gegenbauer polynomials.…
In this paper, we prove two normality criteria for families of some functions concerning shared values, the results generalize those given by Hu and Meng. Some examples are given to show the sharpness of our results.
Higher order derivatives of functions are structured high dimensional objects which lend themselves to many alternative representations, with the most popular being multi-index, matrix and tensor representations. The choice between them…
A procedure to obtain differentiation matrices is extended straightforwardly to yield new differentiation matrices useful to obtain derivatives of complex rational functions. Such matrices can be used to obtain numerical solutions of some…
Let $k$ be a natural number and $s$ be real. In the 1-dimensional case, the $k$-th order derivatives of the functions $\lvert x\rvert^s$ and $\log \lvert x\rvert$ are multiples of $\lvert x\rvert^{s-k}$ and $\lvert x\rvert^{-k}$,…
This article deals with the multiple values and algebraic dependences problem of meromorphic mappings sharing moving hyperplanes in projective space. We give some algebraic dependences theorems for meromorphic mappings sharing moving…
Because of the nonlocal properties of fractional operators, higher order schemes play more important role in discretizing fractional derivatives than classical ones. The striking feature is that higher order schemes of fractional…
We compute the variances of sums in arithmetic progressions of generalised k-divisor functions related to certain L-functions in $\mathbb{F}_q(t)$, in the limit as $q\to\infty$. This is achieved by making use of recently established…
This paper is in concern with Cauchy problems involving the fractional derivatives with respect to another function. Results of existence, uniqueness, and Taylor series among others are established in appropriate functional spaces. We prove…
Inner functions are an important and popular object of study in the field of complex function theory. We look at meromorphic inner functions with a given spectrum and provide sufficient conditions for them to have uniformly bounded…
Let h be a complex meromorphic function decomposed in two different ways P(f) and Q(g), where f, g are meromorphic functions and P, Q are rational functions. We follow an approach due to C.-C. Yang, P. Li and K. H. Ha who handle similar…
We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is…
In this paper, we study scalar the forth order linear differential operators over an oriented 2-dimensional manifold. We investigate differential invariants of these operators and show their application to the equivalence problem.