This paper studies q-Ostrowski-type inequalities for functions whose q-derivatives in absolute value are (alpha, m)-convex. By applying q-H & ouml;lder and q-power mean inequalities, several bounds are derived in explicit form. These results extend existing inequalities for convex and q-convex functions. Some numerical examples and applications to special means are included to illustrate the obtained estimates.
In this paper, we introduce an iterative procedure for approximating fixed points of a contraction mapping. We also discuss its stability under mild conditions. By exploring the properties related to uniformly convex Banach spaces, we can establish a collection of convergence outcomes, both weak and strong, about generalized nonexpansive mappings. Numerical examples demonstrate that the proposed method outperforms several existing iterative schemes. We validate our main result by applying it to find an approximate solution of a fractional Volterra-Fredholm integro-differential equation. The findings extend the scope of numerous previously published results.
In this manuscript, we establish a variety of new diamond-alpha dynamic Hardy-Hilbert inequalities on time scales which are defined as a linear combination of the delta and nabla integrals. When alpha = 1 and alpha = 0, then we obtain some well-known time-scale delta inequalities and nabla inequalities respectively due to Hilbert. These inequalities broaden and combine a variety of continuous inequalities with their discrete literary counterparts. These inequalities generalize and extend existing results in the literature. We use H & ouml;lder's inequality on time scales and a few algebraic inequalities to demonstrate our conclusions.
In the present investigation, we define a certain subfamily of Bazilevic and non-Bazilevic bi-univalent functions involving Bernoulli polynomials to investigate the upper bounds of the initial Taylor-Maclaurin coefficients and the Fekete-Szeg & ouml; functional for functions in this subfamily. In addition, corresponding results have also been obtained for some special cases of this subfamily.
This paper addresses the synchronization problem of the coronary artery system (CAS), a model representing muscular blood vessels. Specifically, the coronary artery refers to the blood vessels responsible for delivering oxygen and nutrients to the heart. Various unpredictable factors, such as thyroid disorders, high blood pressure, and heart valve issues, can cause fluctuations in the internal pressure and diameter of these vessels. As a result, this can lead to severe conditions such as myocardial infarction, abnormal heart rhythms, and other complications. To alleviate these symptoms, a non-fragile controller is developed to synchronize the diseased system with the healthy coronary artery system. By utilizing Lyapunov-Krasovskii functionals (LKFs), Wirtinger's integral inequality, an fragmented-component-based integral inequality, an extended reciprocally convex matrix inequality, and the convex combination method, less conservative synchronization criteria are formulated in the form of Linear Matrix Inequalities (LMIs). In addition, a non-fragile state feedback controller is proposed for CAS to ensure that the resulting closed-loop system satisfies the extended dissipativity condition. By appropriately selecting the weighting matrices, the proposed control scheme is capable of addressing a range of non-fragile performance requirements for CAS, including 2- pound pound infinity performance, H infinity performance, passive performance, mixed H infinity/ passivity performance, and general dissipative characteristics. Two numerical simulations are presented to verify the effectiveness of the proposed method. The first example showcases synchronization under varying time delays and disturbances, while the second example applies the extended dissipative performance to the coronary artery system.
In this article, we first derive the Shur inequality and then explore related Jensen-type inequalities for the recently generated category of (h, m)-convex functions. Some previously missing algebraic properties of convexity are presented to enrich the theory. The main findings are investigated through the application of submultiplicative and supermultiplicative functions. These results expand and generalize respective inequalities for different categories of convex functions that exist in the literature.
A linearized symmetry condition is an expression that enables one to derive symmetries of a given difference equation. Symmetries are utilized to reduce the order and eventually obtain analytical solutions. In this study, we apply this method to a family of higher order difference equations and we present formulas for the solutions of this family. Naturally, the formulas for the solutions pave the way for the study of the periodic nature of these solutions and the stability of the equilibrium points. This work generalizes and extends some results in the literature.
The present study investigates the adaptive hybrid synchronization of a hyperchaotic financial system with unknown parameters. The nonlinear model adopted to describe the complex interactions between the key financial variables such as interest rate, investment demand, price index and market confidence can display hyperchaotic behavior under certain circumstances. To control the complex dynamics of the hyperchaotic financial system, adaptive hybrid synchronization has been proposed between the driving and responding systems. This concept combines complete and anti-synchronization. Lyapunov stability theory has been adopted to obtain adaptive control and parameters to ensure the global asymptotic stability of the error and adaptive estimation parameters. This has been demonstrated for two cases of sign configurations of the adaptive estimation parameters. Simulation results have been provided to support the effectiveness of the proposed method to regulate hyperchaotic financial systems.
We consider a Liouville-Caputo type nonlinear fractional differential equation of order q is an element of (2,3] supplemented with perturbed nonlinear non-separated fractional integral boundary conditions. We present the criteria ensuring the existence and uniqueness of solutions for the given problem. We also discuss the Ulam-Hyers stability for the problem at hand. Then, we extend our discussion to the case of Riemann-Liouville perturbed nonlinear non-separated fractional integral boundary conditions. Examples are offered for illustration of the main results. It is found that some new results appear as special cases of the ones presented in this article.
We introduce a new subclass of k-starlike functions associated with the Rabotnov fractional exponential function. For this class, we determine coefficient estimates, and identify extreme points. Making use of the coefficient estimates and the properties of Rabotnov fractional exponential functions, we discuss the theoretical constructs and their applications to practical tasks in image processing, including edge detection, denoising, and texture analysis. (c) 2026 All rights reserved.
In this note, we mainly study the arithmetic-geometric mean and Cauchy-Schwarz matrix norm inequalities. By using the generalized Holder inequality for symmetric gauge functions, we obtain a more general version of a norm inequality for positive real numbers alpha, beta, gamma and r satisfying 1/alpha + 1/beta= 1/gamma and r > max{ 1/alpha, 1/beta }. The obtained result generalizes the inequalities of Audenaert [K. M. R. Audenaert, Oper. Matrices, 9 (2015), 475-479], Zou [L. Zou, Linear Algebra Appl., 562 (2019), 154-162] and Zou and Jiang [L. Zou, Y. Jiang, J. Math. Inequal., 10 (2016), 1119-1122].
Quadratic stochastic operators (QSOs) arise naturally in population genetics and other areas to model the evolution of probability distributions. While the finite-dimensional theory has been studied extensively, the infinite-dimensional setting poses new challenges and exhibits behavior not seen in finite dimensions. In this paper we collect some basic definitions, recall the notion of a Lyapunov function for a QSO, and present two illustrative examples on the infinite-dimensional simplex. The first example is the shift operator, which is dissipative and has no fixed points. The second example is a Volterra-type operator that allocates cross terms to the smaller index; it is a genuine quadratic stochastic operator and its trajectories converge to a vertex determined by the initial support. We then introduce two new families of quadratic stochastic operators, namely the alpha-replicator family and a weighted replicator family, and analyze their asymptotic behavior. For both the motivating examples and the new families, we compute trajectories from a given initial distribution, tabulate the first few iterates, and plot the coordinates as functions of the iteration number. These computations highlight the rich dynamical phenomena that may arise on the infinite-dimensional simplex.
In this work, we propose the multiplicative version of the Milne quadrature rule and investigate the appropriate concept of convexity within the multiplicative calculus setting. Based on this, we establish a novel fractional identity, which serves as a cornerstone for deriving Milne-type inequalities using multiplicative Riemann-Liouville fractional integrals. To our knowledge, this study is the first to combine fractional calculus with multiplicative analysis in the context of integral inequalities, offering a new approach to non-Newtonian mathematical systems. The results contribute to the development of generalized calculus and pave the way for future research on multiplicative fractional inequalities.
In 1979, L. Carlitz introduced the degenerate Stirling, Bernoulli, and Eulerian numbers in Util. Math. Since then, degenerate versions of special polynomials and numbers have been introduced by many researchers, and the properties of these polynomials and numbers have been investigated. Kim and Kim defined the lambda-analogue of r-Stirling numbers of the second kind, and gave the recurrence relations for these numbers. The purpose of this paper is to derive some interesting identities related to the degenerate Stirling numbers of the first and second kind, degenerate r-Stirling numbers of the second kind, falling factorial sequences, harmonic numbers and Gindalrae-Stirling numbers of the first kind using binomial transform. Furthermore, the shape change of the degenerate r-Stirling number S(r) 2,lambda (k, n) with respect to lambda was demonstrated using Mathematica.
Despite the huge efforts to develop and administer vaccines worldwide to cope with the COVID-19 pandemic, misinformation spreading through fake news in media and social networks about vaccination safety makes people refuse to be vaccinated, which harms not only these people but also the whole population. In this work, we propose a mathematical model to study the effects of harmful information spreading in immunization acquisition through vaccination. As this spreading exhibits memory and persistence effects, our model is equipped to handle several fractional derivatives, including Caputo, Caputo-Fabrizio, Atangana-Baleanu, and fractal-fractional operators, which are well-suited to describe nonlocal interactions and long-term behavioral influences. We provide a unified fractional modeling framework and an analysis of the existence, positivity, and stability of the solutions, as well as the derivation of reproduction and strength numbers that quantify the impact of misinformation. We set the stability conditions by using Lyapunov methods. We have also provided numerical simulations that confirm our analytical findings and illustrate the dynamics of the system in terms of the fractional derivative use and its fractional derivative order. With this model, we facilitate the understanding and mitigation of the impact of harmful information on vaccination campaigns. (c) 2025 All rights reserved.
In this work, we study the stability properties of mild solutions associated with a wide range of nonlinear integro-differential evolution equations defined in Banach spaces. Utilizing Banach's fixed point principle, we establish sufficient criteria ensuring the existence of both Ulam-Hyers stability and Ulam-Hyers-Rassias stability. To substantiate the theoretical findings, we provide several illustrative examples that demonstrate the correctness of the obtained results.
Sufficient conditions for Ulam-Hyers and Ulam-Hyers-Rassias stability of second-order nonlinear quantum difference equations generated by a general quantum difference operator are given. This operator is an extension of the well-known Jackson q-difference and Hahn difference operators. At the end of the paper, an explanatory example is exhibited to demonstrate the applicability of the theoretical results.
