This paper introduces a novel subclass of analytic functions defined by the product of a modified sigmoid function and the lemniscate Bernoulli func-tion. We initiate the study by deriving initial coefficient bounds for functions within this subclass, followed by an investigation into several key analytic prop-erties. Specifically, we establish the Fekete-Szego & uml; inequality and analyze Hankel determinants of various orders. Furthermore, the study provides estimates for the logarithmic coefficients and establishes bounds for both the inverse coefficients and the logarithmic inverse coefficients of functions in the subclass. This compre-hensive analysis offers a significant contribution to the theory of analytic function subclasses associated with the products of special functions.
The objective of our research is to investigate the existence, attractivity and controllability of solutions for integro-differential equations with state-dependent delays. We employ a fixed point theorem to establish the existence of these solutions, while also utilizing the concept of measures of noncompactness. In the last section, we give an example to show that the assumed conditions can be verified and to illustrate our results.
In this paper, we study the optimal control of a nonlinear parabolic problem with missing data. Using the concepts of no-regret control, low-regret control and adapted low-regret control, we give a characterization of the con-trol for ill-posed problems. More precisely, we study the control of a nonlinear parabolic problem using a regularization approach that generates incomplete in-formation. We obtain a singular optimality system characterizing the no-regret control for the nonlinear parabolic problem.
The current study focuses on obtaining the sharp coefficient estimates and Fekete-Szego & uml; inequality for the class Psi(& vartheta;) (m, lambda) and uses the Poisson distribution series to obtain the sharp estimates of coefficient inequalities, Fekete-Szego & uml; inequality, second order Toeplitz determinants and upper bounds of third order Toeplitz determinants and second order Hankel determinants for a certain analytic function U(z) = z + delta(2)z(2) + delta(3)z(3) + & centerdot;& centerdot; & centerdot;, U(z) =/ 0, z is an element of triangle belonging to the class P Psi(& vartheta;)(m, lambda, Upsilon) = {U is an element of H: (IU)-U-k is an element of Psi(& vartheta;)(m, lambda)}, m is an element of N-0 = {0, 1, 2, & centerdot; & centerdot; & centerdot; }, lambda, & vartheta; is an element of N = {1, 2, ...}, Upsilon = Upsilon(i)(k) =k(i-1)/(i-1)! e(-k), defined on the open unit disc (z is an element of triangle :={z : |z| < 1}). This research could motivate others to delve deeper into the coefficient functional problem related to the Poisson distribution series of analytic functions across different categories of univalent functions.
This paper investigates a class of neutral-type fractional differential equations with finite delays, formulated through the generalized Psi-Hilfer fractional derivative. This operator, being a broad framework that unifies various fractional derivatives, is highly effective in modeling dynamical processes with memory and hereditary characteristics. The primary objective is to establish sufficient conditions for the existence and uniqueness of solutions to such equations. The analysis employs fixed point theory-specifically Banach's contraction principle and Krasnoselskii's fixed point theorem-within an appropriately weighted function space. These tools ensure that the solutions are not only well-defined but also uniquely determined. Furthermore, two stability notions, namely Ulam-Hyers stability and its generalized form, are studied to verify that solutions remain close to the expected behavior under small perturbations in initial conditions or parameters. To demonstrate the applicability of the theoretical framework, an illustrative example with explicit functions and parameters is provided. The results strengthen the theoretical foundations of fractional calculus and open directions for further research on more generalized and complex delayed fractional systems.
