Allen, Robert Heller, Katherine Pons, Matthew
Published in
Open Mathematics

Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces . Specifically we study differences of composition operators on the Dirichlet space and S 2, the space of analytic functions whose first derivative is in H 2, and then use Calderón’s complex interpolation to extend the results to the genera...

Han, Caihong Li, Lue Su, Guangwang Sun, Taixiang
Published in
Open Mathematics

Difference equations are often used to create discrete mathematical models. In this paper, we mainly study the dynamical behaviors of positive solutions of a nonlinear fuzzy difference equation: x n + 1 = x n A + B x n − k ( n = 0 , 1 , 2 , … ) , {x}_{n+1}=\frac{{x}_{n}}{A+B{x}_{n-k}}\hspace{0.33em}\left(n=0,1,2,\ldots ), where parameters A , B A,B...

Ikikardes, Nazli Yildiz Hwang, Jihyun Kim, Daeyeoul
Published in
Open Mathematics

The aim of this paper is to find arithmetic convolution sums of some restricted divisor functions. When divisors of a certain natural number satisfy a suitable condition for modulo 12, those restricted divisor functions are expressed by the coefficients of certain eta quotients. The coefficients of eta quotients are expressed by the sine function a...

Olteanu, Octav
Published in
Open Mathematics

First, this work provides an overview of some of the Hahn-Banach type theorems. Of note, some of these extension results for linear operators found recent applications to isotonicity of convex operators on a convex cone. Next, the work investigates applications of the Krein-Milman theorem to representation theory and elements of Choquet theory. A s...

Ji, Zhanjiang
Published in
Open Mathematics

In this paper, we introduce the concepts of G G -Lipschitz tracking property and G G -asymptotic tracking property in metric G G -space and obtain the equivalent conditions of G G -asymptotic tracking property in metric G G -space. In addition, we prove that the self-map f f has the G G -Lipschitz tracking property if and only if the shift map σ \s...

Choi, SoYoung Kim, Chang Heon
Published in
Open Mathematics

Extending our previous work we construct weakly holomorphic Hecke eigenforms whose period polynomials correspond to elements in a basis consisting of odd and even Hecke eigenpolynomials induced by only cusp forms. As an application of our results, we give an explicit construction of the holomorphic parts of harmonic weak Maass forms that are good f...

Liu, Yongfang Zhu, Chaosheng
Published in
Open Mathematics

In this paper, we introduce a new metric space called the mixed-norm Lebesgue space, which allows its norm decay to zero with different rates as ∣ x ∣ → ∞ | x| \to \infty in different spatial directions. Then we study the well posedness for the system of magnetohydrodynamic equations in 3D mixed-norm Lebesgue spaces. By using some fundamental analy...

Alnafisah, Yousef
Published in
Open Mathematics

Davie’s exact coupling technique for stochastic differential equations may be used to enhance the convergence of the multilevel Monte Carlo (MC) methodology. Giles developed the multilevel MC technique, which is based on executing the MC method several times with various time increments. It cuts computing costs significantly by executing most simul...

Ji, Wei
Published in
Open Mathematics

The generic uniqueness of saddle point for two-person zero-sum differential games, within the class of open-loop, against the perturbation of the right-hand side function of the control system is investigated. By employing set-valued mapping theory, it is proved that the majority of the two-person zero-sum differential games have unique saddle poin...

Uzor, Victor Amarachi Alakoya, Timilehin Opeyemi Mewomo, Oluwatosin Temitope
Published in
Open Mathematics

In this paper, we study the problem of finding a common solution of the pseudomonotone variational inequality problem and fixed point problem for demicontractive mappings. We introduce a new inertial iterative scheme that combines Tseng’s extragradient method with the viscosity method together with the adaptive step size technique for finding a com...