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In this paper we correct an inaccuracy that appears in the proof of Theorem 1. in Czerwik's article "Contraction mappings in $b$-metric spaces.", Acta Math. Inform. Univ. Ostraviensis, 1:5--11, 1993., 3 pages

This expository paper presents known results on distribution functions g(x) of the sequence of blocks where xn is an increasing sequence of positive integers. Also presents results of the set G(Xn) of all distribution functions g(x). Specially: - continuity of g(x); - connectivity of G(Xn); - singleton of G(Xn); - one-step g(x); - uniform distribution of Xn, n = 1, 2, . . . ; - lower and upper bounds of g(x); - applications to bounds of ; - many examples, e.g., , where pn is the nth prime, is uniformly distributed. The present results have been published by 25 papers of several authors between 2001-2013.

On a recent paper Benchohra and Mostefai [2] presented some existence results for an integral equation of fractional order with multiple time delay in Banach spaces. In contrast to the classical case, when assumptions are expressed in terms of the strong topology, they considered another case, namely with the weak topology. It has some consequences for the proof. We present here some comments and corrections.

In this paper we improve Theorem 7 in [1] which deals with the existence and uniqueness of solutions of the three dimensional globally modified Navier-Stokes equations.

This note gives the correct form of a result (Theorem 2, p. 478) published recently in [Math. Slovaca 60 (2010), 471–484].

In this paper, we aim to study about the estimation of norm of (p, q)-Bernstein operators B p , q n $\mathcal{B}_{p,q}^{n}$ in C[0,1] for the case q > p > 1 by applying (p, q)-calculus and divided difference analogue of (p, q)-Bernstein operators. Some basic theorem and related results are also discussed in this paper. Here, the extra parameter p shows more flexibility by choosing the value of p.

In this paper, by using Sadovskii’s fixed point theorem and the properties of the measure of noncompactness, we establish some sufficient conditions for the asymptotic stability results of nonlinear neutral integro-differential equations with variable delays. The results presented in this paper improve and generalize some results in the literature. An example is considered to illustrate our main results.

This paper is devoted to a fundamental system of equations in Linear Elasticity Theory: the famous Lamé-Navier system. The Clifford algebra language allows us to rewrite this system in terms of the Euclidean Dirac operator, which at the same time suggests a very natural generalization involving the so-called structural sets. We are interested in finding some structures in the solutions of these generalized Lamé-Navier systems. Using MATLAB we also implement algorithms to compute with such partial differential operators as well as to verify some theoretical results obtained in the paper.

A notion of pentaction of any object in the category $\mathbf{rGr}^{\bullet}$ of reduced groups with action is introduced. The operations are defined in the set $\mathsf{Pentact}(A)$ of pentactions of an object $A$ of $\mathbf{rGr}^{\bullet}$. It is proved that if an object $A$ is perfect with zero weak stabilizer in the sense defined in the paper, then $\mathsf{Pentact}(A)$ is an object of $\mathbf{rGr}^{\bullet}$, it has a derived action on $A$, the object $A$ is action representable and $\mathsf{Pentact}(A)$ represents all actions on $A$., Comment: 20 pages, research paper, LaTeX2e, xypic

In this paper, we deduce the form of a nonconstant meromorphic function f when some power of f shares certain set counting multiplicities in the weak sense with the k-th derivative of the power. The results of this paper generalize the results due to Lahiri and Zeng [Afr. Mat. 27 (2016), 941-947].

This paper aims to show how some standard general results can be used to uncover the spectral theory of tridiagonal and related matrices more elegantly and simply than existing approaches. As a typical example, we apply the theory to the special tridiagonal matrices in recent papers on orthogonal polynomials arising from Jordan blocks. Consequently, we find that the polynomials and spectral theory of the special matrices are expressible in terms of the Chebyshev polynomials of second kind, whose properties yield interesting results. For special cases, we obtain results in terms of the Fibonacci numbers and Legendre polynomials.

In this paper we consider spaces of weight square-integrable and harmonic functions L 2 H(Ω, µ). Weights µ for which there exists reproducing kernel of L 2 H(Ω, µ) are named ’admissible weights’ and such kernels are named ’harmonic Bergman kernels’. We prove that if only weight of integration is integrable in some negative power, then it is admissible. Next we construct a weight µ on the unit circle which is non-admissible and using Bell-Ligocka theorem we show that such weights exist for a large class of domains in ℝ2. Later we conclude from the classical result of reproducing kernel Hilbert spaces theory that if the set {f ∈ L 2 H(Ω, µ)|f(z) = c} for admissible weight µ is non-empty, then there is exactly one element with minimal norm. Such an element in this paper is called ’a minimal (z, c)-solution in weight µ of Laplace’s equation on Ω’ and upper estimates for it are given.

In [S. Yang and Y. Lin, Multilinear strongly singular integral operators with generalized kernels and applications, AIMS Math. 6 2021, 12, 13533–13551], the authors of the present paper further weaken the smoothness condition of kernel functions with multilinear strongly singular Calderón–Zygmund operators of [Y. Lin, Multilinear theory of strongly singular Calderón–Zygmund operators and applications, Nonlinear Anal. 192 2020, Article ID 111699]. They defined a new class of multilinear strongly singular integral operators, and studied its weighted L p {L^{p}} boundedness, variable exponent L p ⁢ ( ⋅ ) {L^{p(\cdot)}} boundedness and endpoint estimates. In this paper, we naturally consider the boundedness of multilinear commutators and multilinear iterated commutators, which are generated by multilinear strongly singular integral operators with generalized kernels and Lipschitz functions. Our results include the corresponding results of multilinear strongly singular Calderón–Zygmund operators and classical multilinear Calderón–Zygmund operators, respectively.

In this paper, we introduce the notion of state monadic BL-algebras and we investigate their properties. We define the concept of state monadic filters and study certain types of state monadic filters; we define and charaterize maximal and prime state monadic filters. Characterizations of local, simple and semisimple state monadic BL-algebras are also explored in the paper as well.

We give a parametrization of square roots of the ideal class of the inverse different of rings defined by binary forms in terms of the orbits of a coregular representation. This parametrization, which can be construed as a new integral model of a “higher composition law” discovered by Bhargava and generalized by Wood, was the missing ingredient needed to solve a range of previously intractable open problems concerning distributions of class groups, Selmer groups, and related objects. For instance, in this paper, we apply the parametrization to bound the average size of the 2-class group in families of number fields defined by binary n-ic forms, where n ≥ 3 {n\geq 3} is an arbitrary integer, odd or even; in the paper [A. Swaminathan, Most integral odd-degree binary forms fail to properly represent a square, preprint 2020], we applied it to prove that most integral odd-degree binary forms fail to primitively represent a square; and in the paper [M. Bhargava, A. Shankar and A. Swaminathan, The second moment of the size of the 2-Selmer group of elliptic curves, preprint 2021], joint with Bhargava and Shankar, we applied it to bound the second moment of the size of the 2-Selmer group of elliptic curves.

In this paper we continue our investigations of 4-dimensional complexes in [A. Cavicchioli, F. Hegenbarth, F. Spaggiari, Four-dimensional complexes with fundamental class, Mediterr. J. Math. 17 (2020), 175]. We study a class of finite oriented 4-complexes which we call FC 4 {\mathrm{FC}_{4}} -complexes, defined as follows. An FC 4 {\mathrm{FC}_{4}} -complex is a 4-dimensional finite oriented CW-complex X with a single 4-cell such that H 4 ⁢ ( X , ℤ ) ≅ ℤ {H_{4}(X,\mathbb{Z})\cong\mathbb{Z}} with a fundamental class [ X ] ∈ H 4 ⁢ ( X , ℤ ) {[X]\in H_{4}(X,\mathbb{Z})} . By well-known results of Wall, any Poincaré complex is of this type. We are interested in two questions. First, for which 3-complexes K does an element [ φ ] ∈ π 3 ⁢ ( K ) {[\varphi]\in\pi_{3}(K)} exist such that K ∪ φ D 4 {K\cup_{\varphi}D^{4}} is a Poincaré complex? Second, if there exists one, how many others can be constructed from K? The latter question was addressed studied in the above cited previous paper of the authors. In the present paper we deal with the first problem, and give necessary and sufficient conditions on K and [ φ ] ∈ π 3 ⁢ ( K ) {[\varphi]\in\pi_{3}(K)} to satisfy Poincaré duality with ℤ {\mathbb{Z}} - and Λ-coefficients. Here Λ denotes the integral group ring of π 1 ⁢ ( K ) {\pi_{1}(K)} . Before, we give a classification of all FC 4 {\mathrm{FC}_{4}} -complexes based on the finite 3-complex K, and make some remarks concerning ℤ {\mathbb{Z}} - and Λ-Poincaré duality.

This paper deals with the approximation properties of a generalized version of Szász–Mirakjan operators which preserve a x {a^{x}} , a > 1 {a>1} (fixed), and x ≥ 0 {x\geq 0} . The uniform convergence of the operators is studied by using some auxiliary results. Also, error estimations are determined by considering the functions from different spaces. The convergence of the said operators is shown and analyzed by graphics. In the same direction, the proposed operators are compared with Szász–Mirakjan operators for the rate of convergence. A Voronovskaya-type theorem is considered and a comparison with Szász–Mirakjan operators is shown in the sense of convexity. To describe the quantitative means of an asymptotic formula, we quantitatively approach the Voronovskaya-type theorem; moreover, a Grüss–Voronovskaya-type theorem is proved. For further investigations regarding the approximation for functions from various spaces, two significant extensions are added keeping in mind some developments in the L p {L_{p}} -space. One is the Kantorovich variant and the other one is the Durrmeyer modification of the defined operators. Here, the rate of convergence is described by means of the function with a derivative of bounded variation for the Durrmeyer modified operators for which some properties are discussed. Also, A-statistical properties of the Durrmeyer modified operators are established. This paper ends by presenting some significant statements and the conclusion.

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 and initial value x − k , x − k + 1 , … , x − 1 , x 0 {x}_{-k},{x}_{-k+1},\ldots ,{x}_{-1},{x}_{0} , k ∈ { 0 , 1 , … } k\in \{0,1,\ldots \} are positive fuzzy numbers. We investigate the existence, boundedness, convergence, and asymptotic stability of the positive solutions of the fuzzy difference equation. At last, we give numerical examples to intuitively reflect the global behavior. The conclusion of the global stability of this paper can be applied directly to production practice.

The aim of this paper is to study the existence and the asymptotic stability of solutions for an epidemiologically emerging reaction-diffusion model. We show that the model has two types of equilibrium points to resolve the proposed system for a fairly broad class of nonlinearity that describes the transmission of an infectious disease between individuals. The model is analyzed by using the basic reproductive number R 0 {R}_{0} . Finally, we present the numerical examples simulations that clarifies and confirms the results of the study throughout the paper.

In 2012, the second author introduced and studied the variety $\mathcal{I}$ of implication zroupoids that generalize De Morgan algebras and $\lor$-semilattices with $0$. An algebra $\mathbf A = \langle A, \to, 0 \rangle$, where $\to$ is binary and $0$ is a constant, is called an \emph{implication zroupoid} ($\mathcal{I}$-zroupoid, for short) if $\mathbf A$ satisfies: $(x \to y) \to z \approx [(z' \to x) \to (y \to z)']'$, where $x' : = x \to 0$, and $ 0'' \approx 0$. Let $\mathcal{I}$ denote the variety of implication zroupoids and $\mathbf A \in \mathcal{I}$. For $x,y \in \mathbf A$, let $x \land y := (x \to y')'$ and $x \lor y := (x' \land y')'$. In an earlier paper we had proved that if $\mathbf A \in \mathcal{I}$, then the algebra $\mathbf A_{mj} = \langle A, \lor, \land \rangle$ is a bisemigroup. In this paper we generalize the notion of semi-distributivity from lattices to bisemigroups and prove that, for every $\mathbf A \in \mathcal{I}$, the bisemigroup $\mathbf A_{mj}$ is semidistributive. Secondly, we generalize the Whitman Property from lattices to bisemigroups and prove that the subvariety $\mathcal{MEJ}$ of $\mathcal I$, defined by the identity: $x \land y \approx x \lor y$, satisfies the Whitman Property., Comment: 11 pages

In a recent paper, [Sarigöl, M. A.: Characterization of summability methods with high indices, Math. Slovaca 63 (2013), 1053–1058], the equivalence ∣C, 0∣ k ⟺ ∣R, pn ∣ k , k ≥ 1, was characterized for infinite single series. In the present paper, this result is extended to doubly summability a different approach.

In a very recent paper, Wang and Bulut [A note on the coefficient estimates of bi-close-to-convex functions, C. R. Acad. Sci. Paris, Ser. I 355 (2017), 876–880] determined the estimates for the general Taylor-Maclaurin coefficients of functions belonging to the bi-close-to-convex function class. In this study, we introduce the class of Libera type bi-close-to-convex functions and obtain the upper bounds for the coefficients of functions belonging to this class. Our results generalize the results in the above mentioned paper.

In their 2012 paper, Bobadilla and Koll\'ar studied topological conditions which guarantee that a proper map of complex algebraic varieties is a topological or differentiable fibration. They also asked whether a certain finiteness property on the relative covering space can imply that a proper map is a fibration. In this paper, we answer positively the integral homology version of their question in the case of abelian varieties, and the rational homology version in the case of compact ball quotients. We also propose several conjectures in relation to the Singer-Hopf conjecture in the complex projective setting., Comment: published/final version

The main objective of this paper is to construct a new sequence of operators involving Apostol-Genocchi polynomials based on certain parameters. We investigate the rate of convergence of the operators given in this paper using second-order modulus of continuity and Voronovskaja type approximation theorem. Moreover, we find weighted approximation result of the given operators. Finally, we derive the Kantorovich variant of the given operators and discussed the approximation results.

In a series of papers, Bamler [Bam20a,Bam20b,Bam20c] further developed the high-dimensional theory of Hamilton's Ricci flow to include new monotonicity formulas, a completely general compactness theorem, and a long-sought partial regularity theory analogous to Cheeger--Colding theory. In this paper we give an application of his theory to lower bounds for the scalar curvatures of singularity models for Ricci flow. In the case of $4$-dimensional non-Ricci-flat steady soliton singularity models, we obtain as a consequence a quadratic decay lower bound for the scalar curvature., 14 pages

Author(s): Bamler, Richard H; Kleiner, Bruce | Abstract: In a recent paper, Brendle showed the uniqueness of the Bryant soliton among 3-dimensional $\kappa$-solutions. In this paper, we present an alternative proof for this fact and show that compact $\kappa$-solutions are rotational symmetric. Our proof arose from independent work relating to our Strong Stability Theorem for singular Ricci flows.

In a recent paper [JUKIĆ, D.: A necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function on a noncompact set, J. Comput. Appl. Math. 375 (2020)], a new existence level was introduced and then was used to obtain a necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function on a noncompact set. In this paper, we determined that existence level for the residual sum of squares of the power-law regression with an unknown location parameter, and so we obtained a necessary and sufficient condition which guarantee the existence of the least squares estimate.

This paper aims at producing numerical solutions of nonlinear parabolic PDEs with forcing term without any linearization. Since the linearization of nonlinear term leads to lose real features, without doing linearization, this paper focuses on capturing natural behaviour of the mechanism. Therefore we concentrate on analysis of the physical processes without losing their properties. To carry out this study, a backward differentiation formula in time and a spline method in space have been combined in leading to the discretized equation. This method leads to a very reliable alternative in solving the problem by conserving the physical properties of the nature. The efficiency of the present method are proved theoretically and illustrated by various numerical tests.

In a recent paper, Sokół et al. [Applications of k-Fibonacci numbers for the starlike analytic functions, Hacet. J. Math. Stat. 44(1) (2015), 121{127] obtained an upper bound for the Fekete-Szegö functionalϕλwhenλ 2R of functions belong to the classSLkconnected withk-Fibonacci numbers. The main purpose of this paper is to obtain sharp bounds forϕλbothλ 2R andλ 2C.

In recent years, the problem of estimating Hankel determinants has attracted the attention of many mathematicians. Their research have been focused mainly on deriving the bounds of H 2 , 2 {H_{2,2}} or H 3 , 1 {H_{3,1}} over different subclasses of 𝒮 {\mathcal{S}} . Only in a few papers third Hankel determinants for non-univalent functions were considered. In this paper, we consider two classes of analytic functions with real coefficients. The first one is the class 𝒯 {\mathcal{T}} of typically real functions. The second object of our interest is 𝒦 ℝ ⁢ ( i ) {\mathcal{K}_{\mathbb{R}}(i)} , the class of functions with real coefficients which are convex in the direction of the imaginary axis. In both classes, we find lower and upper bounds of the third Hankel determinant. The results are sharp.

In this paper, we develop the theory of a class of casual differential equations on a time scale. An existence theorem for casual differential equations on a time scale is given under mixed Lipschitz and compactness conditions by the fixed point theorem in Banach algebra due to Dhage. Some fundamental differential inequalities on a time scale are also presented which are utilized to investigate the existence of extremal solutions. The comparison principle on casual differential equations on a time scale is established. Our results in this paper extend and improve some well-known results.

In this paper, the global exponential stability and periodicity are investigated for delayed neural network models with continuous coefficients and piecewise constant delay of generalized type. The sufficient condition for the existence and uniqueness of periodic solutions of the model is established by applying Banach’s fixed point theorem and the successive approximations method. By constructing suitable differential inequalities with generalized piecewise constant delay, some sufficient conditions for the global exponential stability of the model are obtained. Typical numerical examples with simulations are utilized to illustrate the validity and improvement in less conservatism of the theoretical results. This paper ends with a brief conclusion.

This paper aims at studying the Iwasawa λ-invariant of the p-primary Selmer group. We study the growth behavior of p-primary Selmer groups in p-power degree extensions over non-cyclotomic ℤ p {\mathbb{Z}_{p}} -extensions of a number field. We prove a generalization of Kida’s formula in such a case. Unlike the cyclotomic ℤ p {\mathbb{Z}_{p}} -extension, where all primes are finitely decomposed, in the ℤ p {\mathbb{Z}_{p}} -extensions we consider primes may be infinitely decomposed. In the second part of this paper, we study the relationship of Iwasawa invariants with respect to congruences, obtaining refinements of the results of Greenberg, Vatsal and Kidwell. As an application, we provide an algorithm for constructing elliptic curves with large anticyclotomic λ-invariant. Our results are illustrated by explicit computation.

In this paper we establish general weighted Hardy identities for several subelliptic settings including Hardy identities on the Heisenberg group, Carnot groups with respect to a homogeneous gauge and Carnot–Carathéodory metric, general nilpotent groups, and certain families of Hörmander vector fields. We also introduce new weighted uncertainty principles in these settings. This is done by continuing the program initiated by [N. Lam, G. Lu and L. Zhang, Factorizations and Hardy’s-type identities and inequalities on upper half spaces, Calc. Var. Partial Differential Equations 58 2019, 6, Paper No. 183; N. Lam, G. Lu and L. Zhang, Geometric Hardy’s inequalities with general distance functions, J. Funct. Anal. 279 2020, 8, Article ID 108673] of using the Bessel pairs introduced by [N. Ghoussoub and A. Moradifam, Functional Inequalities: New Perspectives and New Applications, Math. Surveys Monogr. 187, American Mathematical Society, Providence, 2013] to obtain Hardy identities. Using these identities, we are able to improve significantly existing Hardy inequalities in the literature in the aforementioned subelliptic settings. In particular, we establish the Hardy identities and inequalities in the spirit of [H. Brezis and J. L. Vázquez, Blow-up solutions of some nonlinear elliptic problems, Rev. Mat. Univ. Complut. Madrid 10 1997, 443–469] and [H. Brezis and M. Marcus, Hardy’s inequalities revisited. Dedicated to Ennio De Giorgi, Ann. Sc. Norm. Super. Pisa Cl. Sci. (4) 25 1997, 1–2, 217–237] in these settings.

In this paper, we introduce generalizations of rising factorials and falling factorials, respectively, and study their relations with the well-known Stirling numbers, Lah numbers, and so on. The first stage is to define poly-falling factorial sequences in terms of the polyexponential functions, reducing them to falling factorials if k = 1 k=1 , necessitating a demonstration of the relations: between poly-falling factorial sequences and the Stirling numbers of the first and second kind, respectively; between poly-falling factorial sequences and the poly-Bell polynomials; between poly-falling factorial sequences and the poly-Bernoulli numbers; between poly-falling factorial sequences and poly-Genocchi numbers; and recurrence formula of these sequences. The later part of the paper deals with poly-rising factorial sequences in terms of the polyexponential functions, reducing them to rising factorial if k = 1 k=1 . We study some relations: between poly-falling factorial sequences and poly-rising factorial sequences; between poly-rising factorial sequences and the Stirling numbers of the first kind and the power of x x ; and between poly-rising factorial sequences and Lah numbers and the poly-falling factorial sequences. We also derive recurrence formula of these sequences and reciprocal formula of the poly-falling factorial sequences.

In this paper, we provide some conditions for a K-woven pair of K-g-frames to be preserved under an operator and particularly, we report that applying two different operators to a K-woven pair of K-g-frames can leave them K-woven. Several new methods on the construction of K-woven pair of K-g-frames are also given. We end the paper with a new perturbation result on the weaving of K-g-frames, which shows that, under the perturbation condition involved in one known result on this topic, two K-g-frames can be K-woven in the whole space, not merely in the subspace Range(K).

The aim of this paper is to characterize the solutions Φ : G → M 2(ℂ) of the following matrix functional equations Φ ( x y ) + Φ ( σ ( y ) x ) 2 = Φ ( x ) Φ ( y ) , x , y , ∈ G , {{\Phi \left( {xy} \right) + \Phi \left( {\sigma \left( y \right)x} \right)} \over 2} = \Phi \left( x \right)\Phi \left( y \right),\,\,\,\,\,\,x,y, \in G, and Φ ( x y ) − Φ ( σ ( y ) x ) 2 = Φ ( x ) Φ ( y ) , x , y , ∈ G , {{\Phi \left( {xy} \right) - \Phi \left( {\sigma \left( y \right)x} \right)} \over 2} = \Phi \left( x \right)\Phi \left( y \right),\,\,\,\,\,\,x,y, \in G, where G is a group that need not be abelian, and σ : G → G is an involutive automorphism of G. Our considerations are inspired by the papers [13, 14] in which the continuous solutions of the first equation on abelian topological groups were determined.

Multimodal biometric systems are nowadays considered as state of the art subject. Since identity establishment in everyday situations has become very significant and rather difficult, there is a need for reliable means of identification. Multimodal systems establish identity based on more than one biometric trait. Hence one of their most significant advantages is the ability to provide greater recognition accuracy and resistance against the forgery. Many papers have proposed various combinations of biometric traits. However, there is an inferior number of solutions demonstrating the use of fingerprint and finger vein patterns. Our main goal was to contribute to this particular field of biometrics. In this paper, we propose OpenFinger, an automated solution for identity recognition utilizing fingerprint and finger vein pattern which is robust to finger displacement as well as rotation. Evaluation and experiments were conducted using SDUMLA-HMT multimodal database. Our solution has been implemented using C++ language and is distributed as a collection of Linux shared libraries. First, fingerprint images are enhanced by means of adaptive filtering where Gabor filter plays the most significant role. On the other hand, finger vein images require the bounding rectangle to be accurately detected in order to focus just on useful biometric pattern. At the extraction stage, Level-2 features are extracted from fingerprints using deep convolutional network using a popular Caffe framework. We employ SIFT and SURF features in case of finger vein patterns. Fingerprint features are matched using closed commercial algorithm developed by Suprema, whereas finger vein features are matched using OpenCV library built-in functions, namely the brute force matcher and the FLANN-based matcher. In case of SIFT features score normalization is conducted by means of double sigmoid, hyperbolic tangens, Z-score and Min-Max functions. On the side of finger veins, the best result was obtained by a combination of SIFT features, brute force matcher with scores normalized by hyperbolic tangens method. In the end, fusion of both biometric traits is done on a score level basis. Fusion was done by means of sum and mean methods achieving 2.12% EER. Complete evaluation is presented in terms of general indicators such as FAR/FRR and ROC.

Aspace X is said to have the absolutely strongly star -𝒤-Hurewicz (ASS𝒤H) property if for each sequence (𝒰 n : n ∈ 𝕅)of opencovers of X and each dense subset Y of X, there is a sequence (Fn : n ∈ 𝕅) of finite subsets of Y such that for each x ∈ X, {n ∈ 𝕅 : x ∉ St(Fn , 𝒰 n )}∈ 𝒤, where 𝒤 is the proper admissible ideal of 𝕅. In this paper, we investigate the relationship between the ASS𝒤H property and other related properties and study the topological properties of the ASS𝒤H property. This paper generalizes several results of Song [25] to the larger class of spaces having the ASS𝒤H properties.