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.
The primary aim of this scientific note is first to review the essential background on several special functions in which the Gaussian function, in certain complex domains, and its integral play fundamental roles, and subsequently to establish (or organize) a number of relevant results together with some of their potential implications.
This paper investigates certain topological properties of the set of all global solutions for a class of nonlinear 5-Caputo fractional Langevin equations. The nonlinearity, defined on an infinite-dimensional Banach space, is assumed to satisfy Nagumo-type growth conditions. An Aronszajn-type result is established using the nonlinear alternative for condensing operators, combined with the Browder-Gupta method. An illustrative example is provided to support the theoretical findings.
In this paper, we introduce a new and unified subclass of m-fold symmetric bi-univalent functions by subordinating to generalized Janowski function, in the open unit disc E = {z : z < 1}. Bounds for the initial coefficients and Fekete-Szego & uml; inequality for the functions in this class are studied. Particular cases of the results derived here, are also discussed.
We study a class of nonlocal Kirchhoff problems with nonlinearities exhibiting nonstandard growth. Using variational methods in Musielak-Orlicz-Zygmund spaces, we prove the existence of nontrivial weak solutions. The analysis uses generalized N-functions, Orlicz-Zygmund embeddings, pseudo-monotone operators, and the Palais-Smale condition, which allow handling double-phase and nonlocal Kirchhoff terms. The results extend classical variational methods to settings with borderline and logarithmic growth.
We establish the generalized parametric logarithmic Sobolev inequalities in the Gagliardo-Nirenb erg form for variable exponential space with logHo & uml;lder exponential function. Employing the generalized parametric logarithmic Sobolev inequalities, we establish the existence of weak solutions to the boundary problem for the hyperbolic equation with logarithmic nonlinearity and involving variable exponents. Numerical examples and further applications will be addressed in a forthcoming paper.
By employing the A-summation process in the B-statistical sense, where A and B are sequences of infinite matrices, we provide new results on the classical Korovkin theorem for a sequence of monotone and sublinear operators. Reported results essentially extend some theorems existing in the literature.
Although national and international institutions, such as the World Health Organization (WHO) and UNAIDS, are making significant efforts to eradicate HIV by 2030, it remains a major threat to global public health. Despite its low prevalence, HIV continues to claim lives and remains a major public health issue, especially in developing countries. Thanks to the accessibility of antiretroviral drugs, the prevalence of this scourge has been gradually declining worldwide in recent years. Thus, this article investigates the effectiveness of antiretroviral therapy in controlling viral transmission through a fractional-order extension of a deterministic model. We study the boundedness of the model's solution by applying the Laplace transform to solve the fractional Gronwall inequality. To ensure the existence and uniqueness of the model's solution, we rely on the Picard-Lindelo & uml;f theorem. We also study the stability of the disease-free equilibrium point to qualitatively analyze the behavior of the model. Next, we perform a sensitivity analysis of the basic reproduction number R0 to evaluate its robustness concerning the model parameters. Finally, we simulate the approximate solutions of the fractional-order model in MATLAB for different values of the fractional order and present the results of the sensitivity analysis and numerical simulation. Our results demonstrate that the fractional model provides real added value in modeling, thanks to its ability to incorporate memory effects and finely tune transmission dynamics according to the fractional order, thereby allowing for a more realistic representation of epidemiological processes.
Fractional Hermite-Hadamard type inequalities are recognized as significant results in the field of convex analysis. In this work, we derive several inequalities of this type for twice differentiable m-convex functions by employing various analytical methods, including the Ho & uml;lder-I-center dot & cedil;scan inequality and the improved power mean integral inequality.
This paper presents a new computational method based on the Picard iteration method for solving boundary optimal control problems governed by parabolic partial differential equations with two-point boundary conditions. The proposed approach adapts the Picard iteration method to solve the necessary optimality conditions derived from Pontryagin's minimum principle, yielding a solution expressed as a truncated power series. To evaluate the effectiveness of the proposed method, a numerical example is provided, and the obtained results are compared with those derived from an alternative approach, demonstrating the accuracy and reliability of the method.
Let S & lowast; cos be the subclass of starlike functions f associated with cosine function defined by (z f '(z)/f (z)) < cos(z). In this paper, we obtain the sharp coefficient bounds and Hankel determinants of second order for the inverse logarithmic function for this class. We also present the best possible bounds of second order Toeplitz determinant for the functions in the same class.
In this paper, we study the initial boundary value problem involving the p-Laplacian parabolic equation ut-triangle pu + alpha|u|p-2u = 0, (x,t) is an element of ohm & times;]0, +infinity[, with logarithmic boundary condition. By using the potential wells method combined with the Nehari Manifold, we establish the existence of a weak global solution. In addition, we also obtain the decay polynomial of the weak solution. Then, by virtue of the differential inequality technique, we prove that the solutions blow up in finite time under suitable initial values.
This article focuses on a specific Hardy-Hilbert-type integral inequality that is defined in the entire plane. The main contribution is the derivation of a ratio-cosine kernel function, which sets it apart from most existing literature on the subject. As a consequence of the main theorem, a related integral inequality of independent interest is also derived. The exposition is self-contained, with full details of all proofs presented, and each step is carefully justified.
In this paper, we establish a novel Hermite-Hadamard inequality for right and left. Furthermore, some new Hermite-Hadamard type fractional integral inequalities are proved for differentiable functions whose first derivative is (h, m)-convex. We demonstrate that these newly established integral inequalities generalize some existing results. Mathematics Subject Classification (2010): 26A33, 26A51, 26D10, 26D15.
In this paper, we introduce the concepts of (alpha O)-contraction and Reich-type contraction within the framework of complex-valued controlled metric spaces (CVCMS). We also present related fixed point theorems for CVCMS, building on the works considered in the literature review for controlled metric type spaces. To demonstrate the practical implications and significance of our results, we provide several examples and an application in dynamic programming.
In this paper, we obtain several new complete characterizations of pseudolinear functions. Two of the results are of first-order and one is derivative free. The results are derived in terms of the Clarke-Rockafellar subdifferential. Additionally, we prove a characterization of the semistrictly quasilinear functions. It is similar to the derivative free characterization of the pseudolinear functions. We also find the conditions such that a semistrictly quasilinear function become pseudolinear.
