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.
