In this paper, we investigate the Pre-Schwarzian norm estimates for classes of log-harmonic mappings associated with the tanh function. Motivated by earlier studies on sine starlike and sine close-to-starlike log-harmonic mappings, we introduce the class of tanh log-harmonic mappings and determine their radius of starlikeness. Furthermore, we establish sharp upper bounds for the Pre-Schwarzian norm of locally univalent log-harmonic mappings of the form f (z) = h(z)g(z), where h(z) belongs to the class SB & lowast;. As an application, we derive explicit estimates for a special subclass of log-harmonic mappings of the form f(z) = h(z)h '(z).
. This paper provides an analysis of spacetimes characterized by the pseudo W8curvature tensor, with particular focus on their geometric and physical properties within the framework of Einstein's field equations. The study investigates pseudo W8-flat spacetimes as potential Einstein manifolds and examines the associated covariant properties of the energy-momentum tensor, including scenarios with a cosmological constant. It also explores perfect fluid models with vanishing pseudo W8-curvature to understand the behavior of energy density and isotropic pressure, particularly under the timelike convergence condition and its relation to the strong energy condition. Dust-type fluid spacetimes are considered to analyze vacuum solutions with non-zero energy density and their geometric structure. Additionally, the paper constructs explicit spacetime models to illustrate the geometric and physical implications of the vanishing pseudo W8-curvature condition.
. This study seeks to formulate and establish multiple fixed point and common fixed point theorems for a novel class of contractions, called C-type contractions, within the context of S-metric spaces. Furthermore, we provide illustrative examples to substantiate the theoretical findings. The results of this study generalize and extend several previous results in the literature. We use these fixed point results to establish the existence and uniqueness of solutions for a class of conformable differential equations, representing a recent development in fractional calculus.
. In this paper, we focus on constructing analytical asymptotic approximations for solutions of second-order matrix difference operators using the Liouville-Green method. General analytical approximations are provided based on the Discrete Levinson's Fundamental Theorem and Kooman's Theorem. Furthermore, we use the discrete Gronwall inequality to establish error bounds for the asymptotic approximations.
. This paper presents a novel fourth-order two-step iterative method for solving nonlinear equations f (x) = 0, derived by optimizing a key parameter in a combination of established third-order methods. The proposed method enhances efficiency and accuracy, outperforming existing iterative techniques. Extensive numerical experiments on diverse polynomial and transcendental functions demonstrate superior convergence speed and precision. Additionally, the method shows significant promise for applications in polynomiography and broader mathematical analysis, as evidenced by its robust performance in visualization and root-finding tasks.
