Type Theorem Research Articles

On fourth order retarded equations with functional boundary conditions: A unified approach

By means of a recent Birkhoff-Kellogg type theorem, we discuss the solvability of a fairly general class of parameter-dependent fourth order retarded differential equations subject to functional boundary conditions. We seek solutions within a translate cone of nonnegative functions. We provide an example to illustrate our theoretical results.

Liouville type theorems for fractional elliptic systems with coupled terms

Liouville type theorems for fractional elliptic systems with coupled terms

Further Properties of an Operator Commuting with an Injective Quasi-Nilpotent Operator

In (Aiena et al., Math. Proc. R. Irish Acad. 122A(2):101–116, 2022), it has been shown that a bounded linear operator T∈L(X)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T\\in L(X)$$\\end{document}, defined on an infinite-dimensional complex Banach space X, for which there exists an injective quasi-nilpotent operator that commutes with it, has a very special structure of the spectrum. In this paper, we show that we have much more: if a such quasi-nilpotent operator does exist, then some of the spectra of T originating from B-Fredholm theory coalesce. Further, the spectral mapping theorem holds for all the B-Weyl spectra. Finally, the generalized version of Weyl type theorems hold for T assuming that T is of polaroid type. Our results apply to the operators that belong to the commutant of Volterra operators.

Monotonicity and Liouville type theorems of solutions to fully nonlinear fractional problems in the half space

Monotonicity and Liouville type theorems of solutions to fully nonlinear fractional problems in the half space

Fuzzy Korovkin type Theorems via deferred Cesaro and deferred Euler equi-statistical convergence

We establish a fuzzy Korovkin type approximation theorem by using \(eq-stat^{D}_{CE}\)(deferred Ces\'{a}ro and deferred Euler equi-statistical) convergence proposed by Saini et al. for continuous functions over \([a,b]\). Further, we determine the rate of convergence via fuzzy modulus of continuity.

Theorems of Geraghty type generalized F-contraction for dislocated quasi-metric spaces

The generalized F-contraction, Geraghty contraction and admissible function are introduced as the most recent generalizations of the Banach contraction. The presence and uniqueness of fixed points for the newly constructed contraction’s self-mapping on complete metric spaces were investigated. The findings of this article can be interpreted as an improvement on the key findings of the previous article.

On a new approach in the space of measurable functions

In this paper, we present a new modulus of continuity for locally integrable function spaces which is effected by the natural structure of the L_{p} space. After basic properties of it are expressed, we provide a quantitative type theorem for the rate of convergence of convolution type integral operators and iterates of them. Moreover, we state their global smoothness preservation property including the new modulus of continuity. Finally, the obtained results are performed to the Gauss-Weierstrass operators.

Spectrum of quaternion signals associated with quaternion linear canonical transform

In recent years quaternion linear canonical transform (QLCT) has emerged due to its applications in various fields, including image and signal processing. This article discusses two spectrum-related theorems (real Paley–Wiener and Boas type). The real Paley–Wiener type theorem is formulated to describe the character of a compactly supported two-sided quaternion linear canonical transformed (QLCT) signal. The Boas-type theorem is also discussed to explain the property of right-sided QLCT of signals that vanish in the neighborhood of origin. Some potential applications of these theorems on some particular quaternion-type operators are also discussed.

Splitting type results for pseudoconvex domains and remarks on their Nebenhülle

We give a very general splitting type theorem for biholomorphic maps close to identity in the context of smoothly bounded pseudoconvex domains (Theorem 1.4). As a particular case, in the context of worm domains, we essentially reprove the splitting type result (Theorem 1.3) from Bracci et al. (Math Z 292:879–893, 2019) (by a different method). We also discuss some properties of the Nebenhülle of worm domains.

Anisotropic Liouville type theorem for the MHD system in Rn

In this paper we study the Liouville type problem for stationary magnetohydrodynamic equations in Rn. We show that under certain anisotropic integrability conditions on the components of the velocity and the magnetic field the solution is trivial.

The Dabrowski-Sitarz-Zalecki type theorems for six dimensional manifolds with boundary

In this paper, we define the spectral Einstein functionals of spin manifolds with boundary, and we give a complete proof of the Dabrowski-Sitarz-Zalecki type theorem for six dimensional spin manifolds with boundary.

Kuhn–Tucker Type Theorems in Cone and Linear Normed Spaces

Kuhn–Tucker Type Theorems in Cone and Linear Normed Spaces

Entire solutions to the parabolic Monge–Ampère equation with unbounded nonlinear growth in time

The Liouville type theorem on the parabolic Monge–Ampère equation −utdetD2u=1 states that any entire parabolically convex classical solution must be of form −t+|x|2/2 up to a re-scaling and transformation, under additional assumption that partial derivative with respect to time variable ut is strictly negative and bounded. In this paper, we study the case when ut is unbounded, prove an existence result of entire parabolically convex smooth solution and investigate the asymptotic behavior near infinity.

Primes with a missing digit: Distribution in arithmetic progressions and an application in sieve theory

AbstractWe prove Bombieri–Vinogradov type theorems for primes with a missing digit in their ‐adic expansion for some large positive integer . The proof is based on the circle method, which relies on the Fourier structure of the integers with a missing digit and the exponential sums over primes in arithmetic progressions. Combining our results with the semi‐linear sieve, we obtain an upper bound and a lower bound of the correct order of magnitude for the number of primes of the form with a missing digit in a large odd base .

Voronovskaja type theorem for some nonpositive Kantorovich type operators

In this paper we will study a Voronovskaja type theorem and a simultaneous approximation result for a new class of generalized Bernstein operators. The new operators are obtained using a generalization of Kantorovich's method, namely, we will introduce a sequence of operators $K_n^l=D^l\circ B_{n+l}\circ I^l$, where $B_{n+l}$ are Bernstein operators, $D^{l}f=f^{(l)}+a_{l-1}f^{(n-1)}+\dots+a_1f'+a_0f$ is a differential operator with constant coefficients $a_j,\ j\in\{0,\dots,l-1\}$ and $I^{l}$ a corresponding antiderivative operator such that $D^{l}\circ I^{l}=Id$.

Dihedral rigidity in hyperbolic 3-space

We prove a comparison theorem for certain types of polyhedra in a 3-manifold with its scalar curvature bounded below by − 6 -6 . The result confirms in some cases the Gromov dihedral rigidity conjecture in hyperbolic 3 3 -space.

On stable solutions of a weighted elliptic equation involving the fractional Laplacian

In this paper, we study the following fractional Choquard equation with weight where and is a positive weight function satisfying at infinity, for some . We establish, in this paper, a Liouville type theorem saying that if then the above equation has no nontrivial stable solution. Our result, in particular, extends the result in [Le, Phuong. Bull. Aust. Math. Soc. 102 (2020), no. 3, 471–478.] from the Laplace operator to the fractional Laplacian.

Pulsed electromagnetic field coupling to a transmission line with arbitrary loads—A unified methodology based on reciprocity

A unified description of the time-domain (TD) electromagnetic (EM) field coupling to a transmission line (TL) that is terminated by arbitrary linear time-invariant loads is presented. Closed-form expressions for the electric current induced in the loads are derived with the aid of the EM reciprocity theorem of the time-convolution type. The validity of the solution is demonstrated via illustrative numerical examples.

Constructive proofs for localised radial solutions of semilinear elliptic systems on

Ground state solutions of elliptic problems have been analysed extensively in the theory of partial differential equations, as they represent fundamental spatial patterns in many model equations. While the results for scalar equations, as well as certain specific classes of elliptic systems, are comprehensive, much less is known about these localised solutions in generic systems of nonlinear elliptic equations. In this paper we present a general method to prove constructively the existence of localised radially symmetric solutions of elliptic systems on . Such solutions are essentially described by systems of non-autonomous ordinary differential equations. We study these systems using dynamical systems theory and computer-assisted proof techniques, combining a suitably chosen Lyapunov–Perron operator with a Newton–Kantorovich type theorem. We demonstrate the power of this methodology by proving specific localised radial solutions of the cubic Klein–Gordon equation on , the Swift–Hohenberg equation on , and a three-component FitzHugh–Nagumo system on . These results illustrate that ground state solutions in a wide range of elliptic systems are tractable through constructive proofs.

Hopf type theorems for surfaces in the de Sitter–Schwarzschild and Reissner–Nordstrom manifolds

Hopf type theorems for surfaces in the de Sitter–Schwarzschild and Reissner–Nordstrom manifolds