Let \(\Lambda = (\lambda_n)\) be an increasing sequence of non-negative numbers tending to \(+\infty\), with \(\lambda_0 = 0\). We denote by \(S(\Lambda, 0)\) a class of Dirichlet series \(F(s) = \sum_{n=0}^{\infty} f_n \exp\{s \lambda_n\}, \quad s = \sigma + it,\) which have an abscissa of absolute convergence \(\sigma_a = 0\). For \(\sigma < 0\), we define \( M_F(\sigma) = \sup \{|F(\sigma + it)| : t \in \mathbb{R}\}. \) The growth of the function \(F \in S(\Lambda, 0)\) is analyzed in relation to the function \( G(s) = \sum_{n=0}^{\infty} g_n \exp\{s \lambda_n\} \in S(\Lambda, 0), \) via the growth of the function \(1/|M^{-1}_G(M_F(\sigma))|\) as \(\sigma \uparrow 0\). We investigate the connection between this growth and the behavior of the coefficients \(f_n\) and \(g_n\) in terms of generalized orders.

The present paper provides a direct proof of stability of nontrivial nonnegative weak solution for fractional \(p\)-Laplacian problem under concave nonlinearity condition. The main results of this work are extend the previously known results for the fractional Laplacian problem.

In this article we provide classes of hyperbolic chains of inequalities depending on a certain parameter \(n\). New refinements as well as new results are offered. Some graphical analyses support the theoretical results.

In this article, we investigate the power convexity of two generalized forms of the invariant of the contra harmonic mean with respect to the geometric mean, and establish several inequalities involving bivariate power mean as applications. Some open problems related to the Schur power convexity and concavity are also given.

The purpose of this paper is to contribute to the development of the multidual Gamma function. For this aim, we start by defining the multidual Gamma and we propose a multidual analysis technics of in order to show a result regarding real Gamma function.