Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2017
Volume
Vol. 37
Number
No. 2
Description
Journal Volume
Opuscula Mathematica
Vol. 37 (2017)
Projects
Pages
Articles
Non-factorizable C-valued functions induced by finite connected graphs
(2017) Cho, Ilwoo
In this paper, we study factorizability of $C$-valued formal series at fixed vertices, called the graph zeta functions, induced by the reduced length on the graph groupoids of given finite connected directed graphs. The construction of such functions is motivated by that of Redei zeta functions. In particular, we are interested in (i) »non-factorizability« of such functions, and (ii) certain factorizable functions induced by non-factorizable functions. By constructing factorizable functions from our non-factorizable functions, we study relations between graph zeta functions and well-known number-theoretic objects, the Riemann zeta function and the Euler totient function.
Fractional boundary value problems on the half line
(2017) Frioui, Assia; Guezane-Lakoud, Assia; Khaldi, Rabah
In this paper, we focus on the solvability of a fractional boundary value problem at resonance on an unbounded interval. By constructing suitable operators, we establish an existence theorem upon the coincidence degree theory of Mawhin. The obtained results are illustrated by an example.
Existence of three solutions for impulsive nonlinear fractional boundary value problems
(2017) Heidarkhani, Shapour; Ferrara, Massimiliano; Caristi, Giuseppe; Salari, Amjad
In this work we present new criteria on the existence of three solutions for a class of impulsive nonlinear fractional boundary-value problems depending on two parameters. We use variational methods for smooth functionals defined on reflexive Banach spaces in order to achieve our results.
Compact generalized weighted composition operators on the Bergman space
(2017) Hu, Qinghua; Zhu, Xiangling
We characterize the compactness of the generalized weighted composition operators acting on the Bergman space.
Control system defined by some integral operator
(2017) Majewski, Marek
In the paper we consider a nonlinear control system governed by the Volterra integral operator. Using a version of the global implicit function theorem we prove that the control system under consideration is well-posed and robust, i.e. for any admissible control $u$ there exists a uniquely defined trajectory $x_{u}$ which continuously depends on control $u$ and the operator $u\mapsto x_{u}$ is continuously differentiable. The novelty of this paper is, among others, the application of the Bielecki norm in the space of solutions which allows us to weaken standard assumptions.