Inequalities For Functions Research Articles

On Extremal Functions in Inequalities for Entire Functions

On Extremal Functions in Inequalities for Entire Functions

Subclasses of Bi-Univalent Functions Connected with Caputo-Type Fractional Derivatives Based upon Lucas Polynomial

In the current paper, we introduce new subclasses of analytic and bi-univalent functions involving Caputo-type fractional derivatives subordinating to the Lucas polynomial. Furthermore, we find non-sharp estimates on the first two Taylor–Maclaurin coefficients a2 and a3 for functions in these subclasses. Using the values of a2 and a3, we determined Fekete–Szegő inequality for functions in these subclasses. Moreover, we pointed out some more subclasses by fixing the parameters involved in Lucas polynomial and stated the estimates and Fekete–Szegő inequality results without proof.

Some Generalization of Riesz Type Inequalities for Harmonic Mappings on the Unit Disk

In this paper a new generalized norm is defined and Riesz type inequalities for harmonic functions on the unit disk are discussed by applying it. Also sharp constants are obtained for certain special values considered in the reverse case of the standard Riesz inequality.

Riesz Inequality for Harmonic Quasiregular Mappings

In this paper, we generalize the Riesz theorem for harmonic quasiregular mappings for a special case (when p = 2) in the unit disc. Our results improve similar results in this field and are proved with milder conditions. Moreover, we prove another variant forms of Riesz inequality for harmonic quasiregular functions.

Distributed consensus control based on double event-triggered mechanism for multi-agent systems with irregular switching topologies under malicious attacks

This paper studies the consensus control of leader-following multi-agent systems (MASs) with irregular switching communication topology and time-varying delay under malicious attacks. The Markov stochastic process is used to describe the irregular switching of the communication topology caused by random factors, and it is verified that the communication protocol is still feasible when the communication channel is partially broken. At the same time, in order to filter out more efficient status signals and reduce the burden of network communication resources under malicious attacks, the double event-triggered mechanism (DETM) are adopted to make the number of state signals reaching the actuator much less and the state signals more efficient. Then, using the Lyapunov–Krasovskii functional (LKF) and integral inequality methods, the LKF contains the information of the lower bound of delay. Lastly, the stability criterion of MASs stochastic asymptotic consensus with time-varying delay is given, the gain of the consistent controller and the event triggered matrix parameters are solved by using the linear matrix inequality toolbox. Finally, four numerical simulations are given to verify that the MASs with irregular switching topology under malicious attacks can still achieve leader-following consensus.

Socioeconomic differences in limited lung function: a cross-sectional study of middle-aged and older adults in Germany

BackgroundLimited lung function represents a serious health impairment. However, studies investigating social inequalities in limited lung function are rare. Thus, the current study investigates which socioeconomic groups are the most affected by overall limited lung function and severely limited lung function.MethodsData from the population-based German Aging Survey were used (N = 4472), with participants being 40 + years old. Lung function was assessed by the peak flow test. Education, income, and occupational prestige were used as socioeconomic indicators.ResultsWe found that overall limited lung function was highly prevalent across the whole sample, with about 33% (Women: 35%; Men: 30%) having overall limited lung function and 8% (Women: 7%; Men: 8%) having severely limited lung function. Socioeconomic differences in limited lung function emerged for all three indicators, education, income, and occupational prestige, in both men and women in single effect analyses. These differences persisted for occupational prestige and income when controlling for all indicators simultaneously.ConclusionsThus, overall and severely limited lung function are highly prevalent health conditions. Men and women with a low occupational position and those with low income are the most affected. Socioeconomic indicators cannot be used interchangeably when studying health inequalities in lung functioning. Occupational hazards and physical working conditions are likely to constitute major risks of health inequalities in limited lung functioning and should be investigated as such by future studies.

Quantum symmetric integral inequalities for convex functions

In the context of quantum symmetric calculus, this study proposed more refined version of Ostrowski and Hermite–Hadamard type inequalities. The function involved in these inequalities are convex functions. In order to reach the target, left and right quantum symmetric derivative and corresponding integral are used. Furthermore, the Hölder inequality is established in the frame work of left and right quantum symmetric integral. The new results refined the results about integral inequalities that exist in the literature.

The picker routing problem in mixed-shelves, multi-block warehouses

Unlike conventional warehouses, where the inventory of an item is concentrated on a single shelf, the inventory in mixed-shelves warehouses is broken down into units and dispersed throughout the warehouse. As a result, the locations from where items are to be retrieved must be chosen when designing the picker tour. The rare research on the picker routing problem (PRP) in mixed-shelves warehouses focuses on (and heavily exploits the properties of) 1-block warehouses, which are warehouses with only two cross aisles. Here, we tackle the more general PRP in mixed-shelves, multi-block warehouses. To solve the problem, we propose a logic-based Benders decomposition method whereby the master problem selects the locations from where each item is retrieved and the subproblem designs the associated picker tour. We introduce tailored optimality cuts and prove their validity. In addition, we propose a set of various techniques to enhance the performance of the logic-based Benders decomposition, including a lower bounding function and valid inequalities. We show the efficiency and effectiveness of the proposed method through extensive computational experiments carried out on both standard instances from the literature (for the 1-block setting) and newly generated instances (for our case). We also leverage our algorithms to generate managerial insights into the benefits of multi-block layouts and mixed-shelves policies in warehousing.

Some Sharp Bohr-Type Inequalities for Analytic Functions

Some Sharp Bohr-Type Inequalities for Analytic Functions

Some New Estimations of Ostrowski-Type Inequalities for Harmonic Fuzzy Number Convexity via Gamma, Beta and Hypergeometric Functions

This paper demonstrates several of Ostrowski-type inequalities for fuzzy number functions and investigates their connections with other inequalities. Specifically, employing the Aumann integral and the Kulisch–Miranker order, as well as the inclusion order on the space of real and compact intervals, we establish various Ostrowski-type inequalities for fuzzy-valued mappings (F·V·Ms). Furthermore, by employing diverse orders, we establish connections with the classical versions of Ostrowski-type inequalities. Additionally, we explore new ideas and results rooted in submodular measures, accompanied by examples and applications to illustrate our findings. Moreover, by using special functions, we have provided some applications of Ostrowski-type inequalities.

New integral inequalities for synchronous functions via Atangana–Baleanu fractional integral operators

Chebyshev’s inequality is a well-known inequality in the field of inequality theory and yields remarkable results for functions that exhibit synchronous behavior. The study, designed to obtain Chebyshev type inequalities with the help of the Atangana–Baleanu fractional integral operator, which has become the most popular concept of fractional analysis in recent years, aims to obtain general forms for synchronous functions. In the process of obtaining results for synchronized functions within the scope of the study, functional tools such as Atangana–Baleanu fractional integral operator, various mathematical analysis operations and induction were used. The most striking aspect of the findings is that for some special values of the parameter of the fractional integral operator, some of the results can be reduced to the Chebyshev inequality. Compared to the studies in the literature, this study has a unique aspect in that the findings obtained with the help of the Atangana–Baleanu fractional integral operator contain general forms, as well as bringing together a popular concept of synchronous functions and fractional analysis.

Singular value inequalities for submultiplicative and subadditive functions of matrices

Singular value inequalities for submultiplicative and subadditive functions of matrices

Monotonicity patterns and functional inequalities for the Nuttall Q-function

Monotonicity patterns and functional inequalities for the Nuttall Q-function

Stability of Caputa– Hadmmard Fractional Differential Nonlinear ControlSystem with Delay Riemann −Katugampola

This research examines the finite-time stability of a specific category of neural networks with fractional order. Using modified Gronwall inequality and estimations of Mittag–Leffler functions, we provide adequate requirements to guarantee the finite-time stability of neural models with Caputo fractional derivatives. In addition, we have also established insights about the asymptotic stability of fractional-order neural models ,this research examines the Finite-time stability of a specific fractional-order neural network using the "generalized Grunwald inequality". This study introduces the concept of finite-time stability for neural models with fractional derivatives. By utilizing the generalized Gronwall inequality and estimates of Mittag-Leffler functions, sufficient conditions are derived to guarantee the finite-time stability of these models. The study also establishes results regarding the asymptotical stability of fractional-order neural models,our results suggest that our conclusions are more precise than the current literature on stability requirements, and we provide examples demonstrating the proposed theory's significance

New Weighted Inequalities for Functions Whose Higher-Order Partial Derivatives Are Co-Ordinated Convex

The purpose of this study is to establish recent inequalities based on double integrals of mappings whose higher-order partial derivatives in absolute value are convex on the co-ordinates on rectangle from the plane. Also, some special cases of results improved in this study are examined.

Hermite–Hadamard type inequality for non-convex functions employing the Caputo–Fabrizio fractional integral

Hermite–Hadamard type inequality for non-convex functions employing the Caputo–Fabrizio fractional integral

Some Turan-type inequalities for a class of rational functions with prescribed poles

In this paper we prove some results for rational functions with t-fold zeros at the origin and thereby obtain generalizations and refinements of some known inequalities for rational functions. These results in particular yield the improvement and generalizations of some polynomial inequalities.

Exponential stability of periodic solutions for a hematopoiesis model with two time delays

In applied mathematics, many practical problems involving heat flow, species interaction, microbiology, neural networks, and more are associated with delay differential equations. To elucidate regulation and control mechanisms in physiological systems, Mackey and Glass introduced new mathematical models as a representation of hematopoiesis (blood-cell formation) in their influential and highly referenced 1977 paper. The presence of multiple delays, rather than a single delay, can lead to a new range of dynamics: an equation that was stable with one delay may become unstable when the delays are not equal, resulting in sustained oscillations. The dynamics of the non-autonomous Mackey-Glass model with two variable delays have not been thoroughly explored yet, which is presented as an open problem by Berezansky and Braverman. This paper focuses on the existence, uniqueness, and exponential stability of positive periodic solutions of a generalized class of the Hematopoiesis Model with two variable delays. Initially, using properties of cones and a fixed point theorem for a concave and increasing operator, we establish conditions ensuring the existence of a unique positive periodic solution for the model with almost periodic coefficients and delays. Subsequently, we employ a suitable Lyapunov functional method and differential inequality techniques to derive sufficient conditions guaranteeing the exponential stability of the unique positive periodic solution of the system. This approach covers a broad range of models that were previously studied. Additionally, an illustrative example with a numerical simulation is provided to validate the efficiency and reliability of the theoretical results. Our approach can be applied to the case of positive almost periodic solutions and positive pseudo almost periodic solutions of the model under consideration.

Hermite–Hadamard–Mercer-Type Inequalities for Three-Times Differentiable Functions

In this study, an integral identity is given in order to present some Hermite–Hadamard–Mercer-type inequalities for functions whose powers of the absolute values of the third derivatives are convex. Several consequences and three applications to special means are given, as well as four examples with graphics which illustrate the validity of the results. Moreover, several Hermite–Hadamard–Mercer-type inequalities for fractional integrals for functions whose powers of the absolute values of the third derivatives are convex are presented.

Weighted fractional inequalities for new conditions on h-convex functions

We use a new function class called B-function to establish a novel version of Hermite–Hadamard inequality for weighted ψ-Hilfer operators. Additionally, we prove two new identities involving weighted ψ-Hilfer operators for differentiable functions. Moreover, by employing these equalities and the properties of the B-function, we derive several trapezoid- and midpoint-type inequalities for h-convex functions. Furthermore, the obtained results are reduced to several well-known and some new inequalities by making specific choices of the function h.