Related papers: Value sharing by an entire function with its deriv…
The subject of our thesis is the uniqueness theory of meromorphic functions and it is devoted to problems concerning Bruck conjecture, set sharing and related topics. The tool, we used in our discussions is classical Nevanlinna theory of…
Let $G(k)=\int_0^1g(x)e^{kx}dx$, $g\in L^1(0,1)$. The main result of this paper is the following theorem. {\bf Theorem}. {\it If $\limsup_{k\to +\infty}|G(k)|<\infty$, then $g=0$. There exists $g\not\equiv 0$, $g\in L^1(0,1)$, such that…
We prove that, for any positive integer $m$, a segment may be partitioned into $m$ possibly degenerate or empty segments with equal values of a continuous function $f$ of a segment, assuming that $f$ may take positive and negative values,…
We show that degrees containing a complete extensions of arithmetic have the random join property: they are the supremum of any random real they compute, with another random real. The same is true for the truth-table and weak truth-table…
In this paper, we investigate the uniqueness property of meromorphic functions together with its linear difference polynomial sharing two sets. Using the polynomial introduced in [FILOMAT 33(18)(2019), 6055-6072], we have improved the…
Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…
The purpose of the paper is to study the uniqueness problem of a $L$ function in the Selberg class sharing one or two sets with an arbitrary meromorphic function having finite poles. We manipulate the notion of weighted sharing of sets to…
Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.
In this paper, we prove some normality criteria concerning transitivity of normality from one family of meromorphic functions to another which improve and generalize some recent results. We also prove some value distribution results for…
We study properties of arithmetic sets coming from multiplicative number theory and obtain applications in the theory of uniform distribution and ergodic theory. Our main theorem is a generalization of K\'atai's orthogonality criterion.…
This work revolves around the study of differentiability in the Stieltjes sense of a product of functions. A formula for the first order derivative has been obtained in the past, which is similar to the usual one with some extra terms in…
We prove that functions defined on a lattice in a finite dimensional torus with bounded finite differences can be smoothly extended to the whole torus, and relate the bounds on the extension's derivatives with bounds on the original…
An analog of Picard's little theorem for entire functions of matrices is proved.
We establish a Pythagorean theorem for the absolute values of the blocks of a partitioned matrix. This leads to a series of remarkable operator inequalities.
An order theoretic and algebraic framework for the extended real numbers is established which includes extensions of the usual difference to expressions involving $-\infty$ and/or $+\infty$, so-called residuations. Based on this,…
Let $s_0,s_1,s_2,\ldots$ be a sequence of rational numbers whose $m$th divided difference is integer-valued. We prove that $s_n$ is a polynomial function in $n$ if $s_n \ll \theta^n$ for some positive number $\theta$ satisfying $\theta <…
Expressions for the derivatives with respect to order of modified Bessel functions evaluated at integer orders and certain integral representations of associated Legendre functions with modulus argument greater than unity are used to…
In this article, we prove an extension of the mean value theorem and a comparison theorem for subharmonic functions. These theorems are used to answer the question whether we can conclude that two subharmonic functions which agree almost…
A simple statement and accessible proof of a version of the Fundamental Theorem of Asset Pricing in discrete time is provided. Careful distinction is made between prices and cash flows in order to provide uniform treatment of all…
The Implicit and Inverse Function Theorems are special cases of a general Implicit/Inverse Function Theorem which can be easily derived from either theorem. The theorems can thus be easily deduced from each other via the generalized…