Dynamic Inequalities Research Articles

Optimal product release time for a new high-tech startup firm under technical uncertainty

<p style='text-indent:20px;'>Decision makers of new high-tech startup firms always want to choose an optimal time to launch their products which are under research and development (R&D) to obtain the maximum net income of these firms. However, existing models fail to consider the optimal release time of products for these new high-tech startup firms. In this paper, the optimal time to launch the product of the R&D project is assumed to be the first time when the product of the R&D project is released to the market. Based on this assumption, we develop a continuous-time model to find the optimal time at which the startup firm launches its product of the R&D project by considering the price of the similar product. Employing the methods of dynamic programming and variational inequalities, we also provide a closed form solution to our model. We also find that these high-tech startup firms prefer to delay their product release time when the price of the similar product is at a phase of rapid growth or the price has considerable uncertainty. Moreover, some numerical examples are provided to investigate the properties of our model.</p>

OSCILLATION OF SECOND-ORDER HALF-LINEAR NEUTRAL NONCANONICAL DYNAMIC EQUATIONS

In this paper, we shall establish some new criteria for the oscillation of certain second-order noncanonical dynamic equations with a sublinear neutral term. This task is accomplished by reducing the involved nonlinear dynamic equation to a second-order linear dynamic inequality. We also establish some new oscillation theorems involving certain integral conditions. Three examples, illustrating our results, are presented. Our results generalize results for corresponding differential and difference equations.

On some extensions of dynamic Hardy-type inequalities on time scales

The objective of this paper is to establish a new class of dynamic inequalities of the Hardy type which generalize and improve some recent results given in the literature, and we derive some new weighted Hardy type integral inequalities on the time scale.

Dynamic Inequalities of Two-Dimensional Hardy Type via Alpha-Conformable Derivatives on Time Scales

We established some new α-conformable dynamic inequalities of Hardy–Knopp type. Some new generalizations of dynamic inequalities of α-conformable Hardy type in two variables on time scales are established. Furthermore, we investigated Hardy’s inequality for several functions of α-conformable calculus. Our results are proved by using two-dimensional dynamic Jensen’s inequality and Fubini’s theorem on time scales. When α=1, then we obtain some well-known time-scale inequalities due to Hardy. As special cases, we derived Hardy’s inequality for T=R,T=Z and T=hZ. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities.

Dynamic Stochastic Variational Inequalities and Convergence of Discrete Approximation

Dynamic Stochastic Variational Inequalities and Convergence of Discrete Approximation

On Some New Dynamic Inequalities Involving C-Monotonic Functions on Time Scales

In this paper, we establish some new dynamic inequalities involving C-monotonic functions with C≥1, on time scales. As a special case of our results when C=1, we obtain the inequalities involving increasing or decreasing functions (where for C=1, the 1-decreasing function is decreasing and the 1-increasing function is increasing). The main results are proved by applying the properties of C-monotonic functions and the chain rule formula on time scales. As a special case of our results, when T=R, we obtain refinements of some well-known continuous inequalities and when T=N, to the best of the authors’ knowledge, the results are essentially new.

Novel dynamic Hardy‐type inequalities on time scales

In the present article, we proved some new dynamic inequalities of Hardy‐type on an arbitrary time scale. We have used dynamic Minkowski inequality, dynamic Hölder's inequality, dynamic Jensen's inequality and Fubini theorem on time scales to prove our main results. As special case of our results, some Hardy‐type integral inequalities known in the literature have been recaptured, and some original discrete inequalities of Hardy‐type have been established.

Do intergovernmental transfers boost intergenerational income mobility? Evidence from China

Intergenerational income mobility has been widely concerned focusing mainly on the transmission mechanism within families. This paper turns to explore the structural determinants and pays special attentions to the role of intergovernmental transfer. Since the fiscal decentralization in 1990s, intergovernmental transfers become an increasingly critical part in Chinese fiscal system, balancing the fiscal capacities across regions and promoting the equalization of public goods. The question arises naturally as whether transfers targeting at equalization can boost intergenerational mobility. However, little work has investigated this intersection of studies and seldom is known about this question. This paper tries to shed some new lights. Through investigations, it confirms that intergovernmental transfers weaken the income persistence and the effect is especially significant for urban areas; the effects for the rural are mixed. Further explorations indicate that the special-purpose transfer payment has greater effects when measured during college period; notably, entering college may bring the rural children fundamental changes relative to other levels of education. In conclusion, the intergovernmental transfer system is relatively more pro-urban. To better fulfill the equalizing effect of the intergovernmental transfers on both static inequality across regions and dynamic inequality across generations, should the transfers be re-framed with cautions tilting more towards the rural.Meanwhile, the competitive behaviors and (dis)incentives of the local governments should also be taken into accounts.

On Some Generalizations of Integral Inequalities in n Independent Variables and Their Applications

Throughout this article, generalizations of some Grónwall–Bellman integral inequalities for two real-valued unknown functions in n independent variables are introduced. We are looking at some novel explicit bounds of a particular class of Young and Pachpatte integral inequalities. The results in this paper can be utilized as a useful way to investigate the uniqueness, boundedness, continuousness, dependence and stability of nonlinear hyperbolic partial integro-differential equations. To highlight our research advantages, several implementations of these findings will be presented. Young’s method, which depends on a Riemann method, will follow to prove the key results. Symmetry plays an essential role in determining the correct methods for solving dynamic inequalities.

Some New Inverse Hilbert Inequalities on Time Scales

Several inverse integral inequalities were proved in 2004 by Yong. It is our aim in this paper to extend these inequalities to time scales. Furthermore, we also apply our inequalities to discrete and continuous calculus to obtain some new inequalities as special cases. Our results are proved using some algebraic inequalities, inverse Hölder’s inequality and inverse Jensen’s inequality on time scales. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities.

Sensitivity analysis of optimal control problems driven by dynamic history-dependent variational-hemivariational inequalities

The aim of this paper is to investigate a nonlinear optimal control problem governed by a complicated dynamic variational-hemivariational inequality (DVHVI, for short) with history-dependent operators in the framework of an evolution triple of spaces. First, we prove a generalized existence and uniqueness theorem to a class of dynamic variational-hemivariational inequalities, which extends the recent results established by Han-Migórski-Sofonea [12, Theorem 9] and Migórski-Bai [23, Theorem 5]. Then, an optimal control problem driven by a (DVHVI) is studied and an existence theorem is delivered. Finally, we explore the sensitivity properties of the optimal control problem under the consideration depending on the initial data ξ∈H and some further parameter λ∈E.

Some New Bennett–Leindler Type Inequalities via Conformable Fractional Nabla Calculus

In this article, we prove several new fractional nabla Bennett–Leindler dynamic inequalities with the help of a simple consequence of Keller’s chain rule, integration by parts, mean inequalities and Hölder’s inequality for the nabla fractional derivative on time scales. As a result of this, some new classical inequalities are obtained as special cases, and we extended our inequalities to discrete and continuous calculus. In addition, when α=1, we shall obtain some well-known dynamic inequalities as special instances from our results. Symmetrical properties are critical in determining the best ways to solve inequalities.

Diamond-α Hardy-Type Inequalities on Time Scales

In the present article, we prove some new generalizations of dynamic inequalities of Hardy-type by utilizing diamond-α dynamic integrals on time scales. Furthermore, new generalizations of dynamic inequalities of Hardy-type in two variables on time scales are proved. Moreover, we present Hardy inequalities for several functions by using the diamond-α dynamic integrals on time scales. The results are proved by using the dynamic Jensen inequality and the Fubini theorem on time scales. Our main results extend existing results of the integral and discrete Hardy-type inequalities. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities.

Some New Generalizations of Reverse Hilbert-Type Inequalities via Supermultiplicative Functions

Our work in this paper is based on the reverse Hölder-type dynamic inequalities illustrated by El-Deeb in 2018 and the reverse Hilbert-type dynamic inequalities illustrated by Rezk in 2021 and 2022. With the help of Specht’s ratio, the concept of supermultiplicative functions, chain rule, and Jensen’s inequality on time scales, we can establish some comprehensive and generalize a number of classical reverse Hilbert-type inequalities to a general time scale space. In time scale calculus, results are unified and extended. At the same time, the theory of time scale calculus is applied to unify discrete and continuous analysis and to combine them in one comprehensive form. This hybrid theory is also widely applied on symmetrical properties which play an essential role in determining the correct methods to solve inequalities. As a special case of our results when the supermultiplicative function represents the identity map, we obtain some results that have been recently published.

On Some Dynamic (ΔΔ)∇- Gronwall–Bellman–Pachpatte-Type Inequalities on Time Scales and Its Applications

In the present paper, some new generalizations of dynamic inequalities of Gronwall–Bellman–Pachpatte-type on time scales are established. Some integral and discrete Gronwall–Bellman–Pachpatte-type inequalities that are given as special cases of main results are original. The main results are proved by using the dynamic Leibniz integral rule on time scales. To highlight our research advantages, several implementations of these findings are presented. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities.

Weighted dynamic Hardy-type inequalities involving many functions on arbitrary time scales

The objective of this paper is to prove some new dynamic inequalities of Hardy type on time scales which generalize and improve some recent results given in the literature. Further, we derive some new weighted Hardy dynamic inequalities involving many functions on time scales. As special cases, we get continuous and discrete inequalities.

(Δ∇)∇-Pachpatte Dynamic Inequalities Associated with Leibniz Integral Rule on Time Scales with Applications

We prove some new dynamic inequalities of the Gronwall–Bellman–Pachpatte type on time scales. Our results can be used in analyses as useful tools for some types of partial dynamic equations on time scales and in their applications in environmental phenomena and physical and engineering sciences that are described by partial differential equations.

Dynamic Hardy–Copson-Type Inequalities via (γ,a)-Nabla-Conformable Derivatives on Time Scales

We prove new Hardy–Copson-type (γ,a)-nabla fractional dynamic inequalities on time scales. Our results are proven by using Keller’s chain rule, the integration by parts formula, and the dynamic Hölder inequality on time scales. When γ=1, then we obtain some well-known time-scale inequalities due to Hardy. As special cases, we obtain new continuous and discrete inequalities. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities.

Some Generalizations of (∇∇)Δ–Gronwall–Bellman–Pachpatte Dynamic Inequalities on Time Scales with Application

As a new usage of Leibniz integral rule on time scales, we proved some new extensions of dynamic Gronwall–Pachpatte-type inequalities on time scales. Our results extend some existing results in the literature. Some integral and discrete inequalities are obtained as special cases of the main results. The inequalities proved here can be used in the analysis as handy tools to study the stability, boundedness, existence, uniqueness and oscillation behavior for some kinds of partial dynamic equations on time scales. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities.

Ostrowski–Trapezoid–Grüss-Type on (q, ω)-Hahn Difference Operator

We use two parameters for functions whose second (q, ω)-derivatives are bounded in order to prove several recent extensions of the Ostrowski inequality and its companion inequalities on (q, ω)-Hahn difference operator. Furthermore, we procure some q-integral and continuous inequalities as special cases of the main results as well these generalizations. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities.