Acta et Commentationes Universitatis Tartuensis de Mathematica

On a generalization of quasi-metric space

2025-08-21T16:03:15+00:00

We introduce a distinctive metric structure for generalized topology by extending the quasi-metric. This extension (to be called gquasi metric) naturally induces a generalized topology, yet it may diverge from forming a topology. We demonstrate that g-quasi metrizability remains an invariant property of generalized topological spaces. Expanding the concepts of metric product and uniform continuity within g-quasi metric spaces, we observe an instance where a g-quasi metric may not exhibit uniform continuity like standard metrics. Additionally, we study completeness, Lebesgue property, and weak G-completeness for g-quasi metric spaces.

Characterizations of ρ-Einstein solitons on LP-Sasakian manifolds admitting the Zamkovoy connection

2026-02-06T15:14:03+00:00

The purpose of this research is to investigate ρ-Einstein solitons on LP-Sasakian manifolds under certain curvature conditions. The novelty of our research lies in the fact that we characterize ρ-Einstein solitons on LP-Sasakian manifolds equipped with the Zamkovoy connection when the structure vector field is considered as the potential vector field. We obtain some significant results on classifications of ρ-Einstein solitons in regard to the W₈-curvature tensor and the Zamkovoy connection. In extension, we build a non-trivial example of a three dimensional LP-Sasakian manifold endowed with the Zamkovoy connection.

Ricci solitons on spacetimes with the spatially homogeneous rotating metrics

2025-12-06T20:02:41+00:00

This paper investigates Ricci solitons on spacetimes equipped with spatially homogeneous rotating metrics. We systematically classify all vector fields that generate Ricci solitons within this geometric framework. Special attention is devoted to identifying the precise conditions under which these vector fields assume gradient form. Furthermore, we establish that every vector field associated with a Ricci soliton in this setting exhibits conformal Killing properties, revealing a fundamental connection between these geometric structures. Finally, we present an example of the desired space and examine the Ricci solitons on it.

On α-order λ-statistical convergence and some inclusion theorems in non-Archimedean 2-normed spaces

2026-01-30T13:36:52+00:00

This paper introduces the notion of α-order λ-statistical convergence over non-Archimedean 2-normed spaces, with K representing a non-trivially valued, complete non-Archimedean field. Further, properties like linearity, uniqueness of limits, and certain properties of α-order λ-statistical convergence sequences, α-order λ-statistical Cauchy sequences are established in non-classical analysis. Some inclusion theorems are proved, and the concepts of α-order λ-statistical limit superior and α-order λ-statistical limit inferior for sequences in non-Archimedean 2-normed spaces are introduced, along with a discussion of related results.

AT algorithm for fractal polynomiographs: a study on fast convergence under weak contraction mappings

2025-12-08T11:56:28+00:00

In the present work, we use the AT algorithm, an iteration consisting of three steps that approximates the fixed point of a weak contraction. The algorithm not only demonstrates faster convergence compared to established methods such as the S, Normal-S, Varat, Mann, Ishikawa, and Picard iterations for weak contraction, but also exhibits strong convergence properties. The paper also explores the AT algorithm’s almost stable behavior for weak contraction. We further apply the AT iterative scheme to construct Julia sets and polynomiographs, providing a practical comparison with the AET values for the Normal-S, Mann, Picard, and AT iterations, thereby demonstrating the real-world relevance of our research.

Cohomologies and linear deformations of relative Rota–Baxter operators on pre-Jacobi–Jordan algebras

2025-12-21T00:02:15+00:00

The cohomology theory of relative Rota–Baxter operators on pre-Jacobi–Jordan algebras is introduced. The cohomological approach is used to study linear deformations of relative Rota–Baxter operators. In particular, the notion of Nijenhuis elements is introduced to characterize trivial linear deformations

Abundant families of exact solitary wave solutions for the time-fractional Estevez–Mansfield–Clarkson equation

2026-04-04T09:45:00+00:00

The Estevez–Mansfield–Clarkson (EMC) equation is analytically modified to incorporate conformable time-fractional derivatives. This equation serves as a significant model in mathematical physics, optics, and the study of shape evolution in liquid droplets. In this work, the EMC equation is solved using the Jacobi elliptic function expansion method. Various solitary wave solutions such as dark and bright solitons, and multi-wave solutions are derived in terms of rational, hyperbolic, and trigonometric functions. The physical behavior of these solutions is illustrated graphically through contour plots, as well as 2D and 3D visualizations. To confirm the accuracy of the solutions, numerical simulations are conducted. The study concludes with a discussion of the results and final remarks.

The connected niche graphs of split tournaments

2026-01-13T14:47:49+00:00

The niche graph of a digraph D has V (D) as the vertex set and an edge uv if and only if (u, w) ∈ A(D) and (v, w) ∈ A(D), or (w, u) ∈ A(D) and (w, v) ∈ A(D) for some w ∈ V (D). In this paper, we find out the characteristics of the connected graph G and the split tournament D = ST(I ∪ K, A) when G is the niche graph of D.

Closed-form expressions for polylogarithmic integrals and related harmonic sums

2026-02-10T08:15:24+00:00

This paper derives closed-form expressions for a class of five-parameter polylogarithmic integrals, expressed in terms of the polylogarithm and Lerch transcendent, and reducible (under admissible parameter choices) to Riemann and Hurwitz zeta values. The paper further obtains closed forms for related linear Euler-type sums and BBP-type series. All results are established using purely real-analytic methods.

Lacunary strong Riesz summability

2026-03-24T09:15:45+00:00

In this paper, we introduce a new class of sequence spaces N^(k)_θ,Rby combining lacunary block structures with Riesz-type weighted means of order k. This construction extends the classical notion of lacunary strong convergence to a higher-order weighted setting. We establish several inclusion relations between the classical strong Riesz summability method of order k and the corresponding lacunary space N⁽^k⁾_θ,Rin the spirit of Freedman-type comparisons. The sharpness of the obtained conditions is illustrated by appropriate counterexamples. Basic topological properties of the new spaces are also discussed.

A note on attaining diameter two properties in Lipschitz-free spaces

2026-03-03T10:51:20+00:00

We prove that in Lipschitz-free spaces the strong diameter two property, the diameter two property, and the local diameter two property coincide with their corresponding attaining variants.

Stability of properties α and β under absolute sums of Banach spaces

2026-04-24T09:54:09+00:00

We study the stability of properties α and β under absolute sums of two real Banach spaces. We prove that if N is an absolute normalised norm on R² whose unit sphere is polygonal, then X ⊕_N Y has property α whenever both X and Y have property α, and similarly for property β. We also obtain partial converse results. For property α, if (1, 0) is an extreme point of B_{(R², N)} and X ⊕_N Y has property α, then X has property α. For property β, if (1, 0) is not an extreme point of B_{(R², N)} and X ⊕_N Y has property β, then X has property β. As corollaries, we recover the finite ℓ₁- and ℓ_∞-cases and obtain corresponding equivalence results.

Correction to: Convergence analysis of an inertial method for a system of general quasi-variational inequalities under mild conditions

2026-05-09T13:36:52+00:00

This note concerns the paper by S. Jabeen, S. Macías, J. E. Macías-Díaz and S. Ullah, Convergence analysis of an inertial method for a system of general quasi-variational inequalities under mild conditions, Acta Comment. Univ. Tartu. Math. 29 (2025), no. 2, 243-258. We note that the fixed-point reformulation used in that paper does not follow from the stated assumptions, and give a simple two-dimensional example. We also record a separate diffculty in the proof of the convergence theorem: the assumptions on the operators T₁and T₂concern only the first variable, whereas the proof uses estimates in which both variables vary. A one-dimensional example shows that the convergence statement, as stated, is not valid even when the constraint set is the whole real line and the auxiliary mapping is the identity.