Convolution conditions are discussed for the \(q\)-analogue classes of Janowski starlike, convex and spirallike functions.

we discuss a framework for constructing large subsets of \(\mathbb{R}^n\) and \(K^n\) for non-archimedean local fields \(K\). This framework is applied to obtain new estimates for the Hausdorff dimension of angle-avoiding sets and to provide a counterexample to a limiting version of the Capset problem.

Let \( R \) be a commutative ring with unity and \( M \) be an \( R \)-module. The total graph of \( M \) with respect to the singular submodule \( Z(M) \) of \( M \) is an undirected graph \( T(\Gamma(M)) \) with vertex set as \( M \) and any two distinct vertices \( x \) and \( y \) are adjacent if and only if \( x + y \in Z(M) \). In this paper, the author attempts to study the domination in the graph \( T(\Gamma(M)) \) and investigate the domination number and the bondage number of \( T(\Gamma(M)) \) and its induced subgraphs. Some domination parameters of \( T(\Gamma(M)) \) are also studied. It has been shown that \( T(\Gamma(M)) \) is excellent, domatically full, and well covered under certain conditions.

In this paper, we study a class of sequences of polynomials linked to the sequence of Bell polynomials. Some sequences of this class have applications on the theory of hyperbolic differential equations and other sequences generalize Laguerre polynomials and associated Lah polynomials. We discuss, for these polynomials, their explicit expressions, relations to the successive derivatives of a given function, real zeros and recurrence relations. Some known results are significantly simplified.

We show that if \( G \) is a discrete Abelian group and \( A \subseteq G \) has \( \|1_A\|_{B(G)} \leq M \), then \( A \) is \( O(\exp(\pi M)) \)-stable in the sense of Terry and Wolf.