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 T1 and T2 concern 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.
. The purpose of this research is to investigate rho-Einstein solitons on LP-Sasakian manifolds under certain curvature conditions. The novelty of our research lies in the fact that we characterize rho-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 rho-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.
In this paper, we introduce a new class of sequence spaces N-theta,R((k)) by 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-theta,R((k)) in 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.
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.
The niche graph of a digraph D has V (D) as the vertex set and an edge uv if and only if (u, w) E A(D) and (v, w) E A(D), or (w, u) E A(D) and (w, v) E A(D) for some w E V (D). In this paper, we find out the characteristics of the connected graph G and the split tournament D = ST (I U K, A) when G is the niche graph of D.
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.
. 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.
. We study the stability of properties cx and /3 under absolute sums of two real Banach spaces. We prove that if N is an absolute has property cx whenever both X and Y have property cx, and similarly for property /3. We also obtain partial converse results. For property cx, if (1,0) is an extreme point of B(R2,N) and X circle plus N Y has property cx, then X has property cx. For property /3, if (1,0) is not an extreme point of B(R2,N) and X circle plus N Y has property /3, then X has property /3. As corollaries, we recover the finite & ell;1- and & ell;infinity-cases and obtain corresponding equivalence results.
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.
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.
This paper introduces the notion of cx-order A-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 cx-order A-statistical convergence sequences, cx-order A-statistical Cauchy sequences are established in non-classical analysis. Some inclusion theorems are proved, and the concepts of cx-order A-statistical limit superior and cx-order A-statistical limit inferior for sequences in non-Archimedean 2-normed spaces are introduced, along with a discussion of related results.
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.
We find an extension of the quasi-metric (to be called $g$-quasi metric) such that the induced generalized topology may fail to form a topology. We show that $g$-quasi metrizability is a $g$-topologically invariant property of generalized topological spaces. Extending metric product and uniform continuity for $g$-quasi metric spaces, we note that a $g$-quasi metric may fail to be uniformly continuous in the extended sense unlike usual metric. Finally, we extend the study of completeness, Lebesgue property and weak $G$-completeness for $g$-quasi metric spaces.
In connection to Brück conjecture we improve a uniqueness problem for entire functions that share a polynomial with linear differential polynomial.
We investigate hypersurfaces in the four-dimensional Thurston geometry Nil3 × R, by giving a complete classification of hypersurfaces whose second fundamental form is a Codazzi tensor, they are either parallel or totally geodesic. Furthermore, we prove that the totally umbilical hypersurfaces in Nil3 × R are totally geodesic.
In this article, we studied the Diophantine equation ax + 8y = z2, where a is a fixed positive integer with a ≡ 3 (mod 4) and x, y, z are non-negative integers. The results show all non-negative integer solutions of this Diophantine equation.
In connection to Bruck conjecture we improve a uniqueness problem for entire functions that share a polynomial with linear differential polynomial.
In this study, we propose the idea of crossed homomorphisms between Lie–Yamaguti superalgebras and develop the Yamaguti cohomology theory of crossed homomorphisms. In light of this, we characterize linear deformations of crossing homomorphisms between Lie–Yamaguti superalgebras using this cohomology. We demonstrate that if two linear or formal deformations of a crossing homomorphism are similar, then their infinitesimals are in the same cohomology class in the first cohomology group. In addition, we show that an order n deformation of a crossing homomorphism can be extended to an order n+1 deformation if and only if the obstruction class in the second cohomology group is trivial.
In this paper, we design some generalized split problems which can be seen as an extended form of the split variational inequality problems. We present several iterative algorithms for solving generalized split problems and demonstrate the weak convergence results under some appropriate assumptions within the context of real Hilbert spaces. Finally, we support these results with the help of numerical examples in both the finite and infinite dimensional spaces. As a result of this work, a new direction will be opened in studying split problems.
We investigate hypersurfaces in the four-dimensional Thurston geometry Nil3 x R, by giving a complete classification of hypersurfaces whose second fundamental form is a Codazzi tensor, they are either parallel or totally geodesic. Furthermore, we prove that the totally umbilical hypersurfaces in Nil3 x R are totally geodesic.
