Related papers: On The Problem Of Entire Functions That Share a Sm…
In this note we discuss some formal properties of universal linearization operator, relate this to brackets of non-linear differential operators and discuss application to the calculus of auxiliary integrals, used in compatibility…
In the paper, concerning a question of Yi [23], we study general criterion for the uniqueness of an L-function and a general meromorphic function. Our results improve and extend all the existing results in this direction [23, 18, 17, 4] to…
In this paper, we study uniqueness problems for entire functions that partially share two values with their higher-order derivatives. The results obtained here both improve and generalize the related results of Li and Yi \cite{LYi}, L\"{u}…
This short note provides a sharper upper bound of a well known inequality for the sum of divisors function. This is a problem in pure mathematics related to the distribution of prime numbers. Furthermore, the technique is completely…
We describe an inequality of finite or infinite sequences of real numbers and their quotients. More precisely, we compare the quotient of H\"older functionals of two sequences of numbers with the sum of their quotients. In the last section…
Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…
We investigate microlocal properties of partial differential operators with generalized functions as coefficients. The main result is an extension of a corresponding (microlocalized) distribution theoretic result on operators with smooth…
Inverse spectral problems are studied for the second order integro-differential operators on a finite interval. Properties of spectral characteristic are established, and the uniqueness theorem is proved for this class of inverse problems.
We study generic holomorphic families of dynamical systems presenting problems of small divisors with fixed arithmetic. We prove that we have convergence for all parameter values or divergence everywhere except for an exceptional set in the…
This paper is devoted to the uniqueness problem of the power of a meromorphic function with its differential polynomial sharing a set. Our result will extend a number of results obtained in the theory of normal families. Some questions are…
We establish the unique solvability of a coupling problem for entire functions which arises in inverse spectral theory for singular second order ordinary differential equations/two-dimensional first order systems and is also of relevance…
The aim of this paper is to define a new operator by using the generalized Struve functions. By using this operator we define a subclass of analytic functions. We discuss some properties of this class such as inclusion problems, radius…
In this paper, we solve certain Fermat-type partial differential-difference equations for finite order entire functions of several complex variables. These results are significant generalizations of some earlier findings, especially those…
In this paper we present equivalence results for several types of unbounded operator functions. A generalization of the concept equivalence after extension is introduced and used to prove equivalence and linearization for classes of…
In this paper, we derive a generalized multiplicative Hardy-Littlewood-Polya type inequality, as well as several related additive inequalities, for functions of operators in Hilbert spaces. In addition, we find the modulus of continuity of…
A new class of functions with a unique identification minor is introduced: functions determined by content and singletons. Relationships between this class with other known classes of functions with a unique identification minor are…
In this paper, we investigate the complete monotonicity of some functions involving gamma function. Using the monotonic properties of these functions, we derived some inequalities involving gamma and beta functions. Such inequalities…
We study infinite order differential operators acting in the spaces of exponential type entire functions. We derive conditions under which such operators preserve the set of Laguerre entire functions which consists of the polynomials…
Starting with a question of Yuan-Li-Yi [Value distribution of L-functions and uniqueness questions of F. Gross, Lithuanian Math. J., 58(2)(2018), 249-262] we have studied the uniqueness of a meromorphic function f and an L-function L…
In this work we establish a connection between two classical notions, unrelated so far: Harmonic functions on the one hand and absolutely monotonic functions on the other hand. We use this to prove convexity type and propagation of…