Band 75, Heft 2

This article introduces a weak difference on a poset as a generalization of a difference on a poset and deals with connections between weak differences and weak BCK-algebras. In particular, conditions under which a poset with a certain weak difference is a meet semilattice are provided. These conditions are then applied to some partial orders on rings, namely the weak right star order and the strong right star order on a right-strong Rickart ring, as well as the sharp order on a certain subset of an arbitrary unitary ring.

A weaker variant of κ -compactness is introduced and investigated, namely, weak κ -compactness, where κ is a regular uncountable cardinal. It is shown that these two notions coincide when κ is a strongly compact cardinal. The existence of a weakly κ -compact extension for a Tychonoff space is proved. Weak κ -compactness can also be defined by demanding that a certain equivalence holds between certain classes of Baire measures. Finally, κ -measure-compact spaces are introduced and studied.

In the present investigation, we determine various radius constants for the class S * ( β ) of starlike functions of order β : We define S λ,β to be the class of normalised analytic functions f satisfying Re(e i λ (1 − z ) 1+ β f ( z )/ z ) > 0 and introduce a product function G ( z ) := (1 −z ) 1+ β g 1 ( z ) g 2 ( z ) =z with g 1 , g 2 ∈ S λ,β , to find radius constants for G ( z ) to be in certain desired classes. Notably, earlier known results are identified herein as special cases of our findings and all the results obtained are sharp.

In this paper, we study maximal subextension of m -subharmonic functions with given boundary values. We also prove stability in m -capacity of maximal subextension of m -subharmonic functions with given boundary values.

This work is devoted to the nonlinear fractional differential equations of arbitrary order, considering the Riemann-Liouville derivative. We extend well-known oscillation criteria for super-linear integer-order differential equations. Finally, we show some discrepancies between the asymptotic behavior of solutions for fractional and integer order case.

In this paper, the third-order delay differential equation of the form (a2(t)((a1(t)x′(t))′)α)′+b(t)xα(σ(t))=0 $$\Big(a_{2}(t)\big((a_{1}(t)x'(t))'\big)^{\alpha}\Big)'+b(t)x^{\alpha}(\sigma(t))=0$$ under the conditions ∫t0∞1a21/α(t)dt=∞ $\int\limits_{t_{0}}^{\infty}\frac{1}{a_{2}^{1/\alpha}(t)}\text{d} t =\infty \quad$ and ∫t0∞1a1(t)dt<∞ $\int\limits_{t_{0}}^{\infty} \frac{1}{a_{1}(t)}\text{d} t <\infty$ is studied. Our newly proposed approach allow us to reduce the number of conditions required for all solutions of the considered equation to be oscillatory. The results established here are new, improve and complement some oscillation results known for the studied equation. Examples are provided to show the strength and novelty of the results obtained.

In the current paper, we investigate the global dynamics of the following difference equations system of exponential form: Υn+1=Γ1+δ1e−Υn−1Θ1+Ψn,Ψn+1=Γ2+δ2e−Ψn−1Θ2+Ωn,Ωn+1=Γ3+δ3e−Ωn−1Θ3+Υn,n∈N0, $$\begin{equation*} \Upsilon_{n+1}=\frac{\Gamma_{1}+\delta_{1}\text{e}^{-\Upsilon_{n-1}}}{\Theta_{1}+\Psi_{n}}, \quad \Psi_{n+1}=\frac{\Gamma_{2}+\delta_{2}\text{e}^{-\Psi_{n-1}}}{\Theta_{2}+\Omega_{n}}, \quad \Omega_{n+1}=\frac{\Gamma_{3}+\delta_{3}\text{e}^{-\Omega_{n-1}}}{\Theta_{3}+\Upsilon_{n}}, \quad n\in \mathbb{N}_{0}, \end{equation*}$$ where the coefficients Γ p , δ p , Θ p for p ∈ {1, 2, 3} and the initial conditions Υ −s , Ψ −s , Ω −s , for s ∈ {0, 1} are positive constants. Further, a numerical example is presented to confirm the obtained theoretical results.

In this paper, we present new conditions for the oscillation of all solutions of the third-order functional difference equations with semi-canonical operators by transforming the studied equation into canonical type equations. This greatly simplifies to find conditions for the oscillation of all solutions of the studied equation. The results obtained here essentially improve and complement to the ones in Srinivasan et al. (2022). The importance and the novelty of the findings are illustrated with five specific examples.

In this paper, we present new conditions yielding a unique fixed point for non expansive type mappings. We also obtain common fixed point theorems for mappings that not necessarily satisfy any known contractive type conditions. Since general methods for studying common fixed points of non-contractive mappings are not available, our present findings provides a new tools in this direction. Moreover, a common fixed point theorem is used to demonstrate in solving nonlinear integral equation problem.

Hyers-Ulam stability of functional equation in single variable is studied in non-triangular metric spaces. We derive it as applications of some fixed point results developed on the said structure. A general version of Baker’s theorem is also deduced as a consequence.

This article concerns the Herrlich-Chew theorem stating that a Hausdorff zero-dimensional space is ℕ-compact if and only if every clopen ultrafilter with the countable intersection property in this space is fixed. It also concerns Hewitt’s theorem stating that a Tychonoff space is realcompact if and only if every z -ultrafilter with the countable intersection property in this space is fixed. The axiom of choice was involved in the original proofs of these theorems. The aim of this article is to show that the Herrlich-Chew theorem is valid in ZF, but it is an open problem if Hewitt’s theorem can be false in a model of ZF. It is proved that Hewitt’s theorem is true in every model of ZF in which the countable axiom of multiple choice is satisfied. A modification of Hewitt’s theorem is given and proved true in ZF. Several applications of the results obtained are shown.

We compute the complex K-ring of oriented flag manifolds F̃ ( n 1 , … , n k ) , k ≥ 3, of type ( n 1 , … , n k ). We use the representation theory of spinor groups and the Hodgkin spectral sequence for the computation of the K-ring.

In this paper, we study a weaker form of continuity known as split continuous function which was introduced in [Beer et al.: Split Continuity , J. Math. Anal. Appl. 474 (2019), 833–851]. In the first section, we emphasize the pointwise convergence of split continuous functions and characterize the pointwise limit of a sequence of split continuous functions. In the last section, we investigate Cauchy split continuous functions and their related properties.

We prove that both the eta transformation formula and the transformation formula for Dieter’s Lambert series are consequences of the Hecke functional equation for the generating zeta-function. Then using the product expression for the theta-function, we prove the theta-transformation formula under a general modular substitution is a consequence of those two transformation formulas, and consequently, theta transformation formula itself is a consequence of the Hecke modular relation.

We investigate some properties recently studied by Cruz-Castillo, Ramı́rez-Páramo and Tenorio. These properties lie and behave in the middle ground between covering properties (in particular star corvering properties) and variations of separability. This dual perspective opens the door to numerous implications and connections among various known properties. In this paper, we present a few of them.