in this paper, we introduce a satisfaction function (sf) to compare interval values on the basis oftseng and klein’s idea. the sf estimates the degree to which arithmetic comparisons between two intervalvalues are satisfied. then, we define two other functions called lower and upper sf based on the sf. weapply these functions in order to present a new interpretation of inequality constraints wi...

According to the Ahlowalia hypothesis (1995), the growth of total factor productivity (TFP) beside infrastructure investments of government lead to income inequality decrease in rural areas of countries. The main objective of this study is to investigate the effects of public investments such as agricultural R&E, road, education and irrigation on income inequality in rural areas of Iran. In ord...

Two results related to Mulholland inequality are presented. First, there are functions that are not geo-convex but solve Mulholland inequality; thus Mulholland’s condition is not necessary. Second, the set of functions that solve Mulholland inequality is not closed with respect to compositions. As a corollary, the dominance relation on the set of strict triangular norms is not transitive. The p...

* Correspondence: [email protected] Yangtze Center of Mathematics, Sichuan University, Chengdu 610064, China Abstract The aim of this article is to study the attracting and quasi-invariant sets for a class of impulsive stochastic difference equations. By establishing a difference inequality, we obtain the attracting and quasi-invariant sets of systems under consideration. An example is give...

Recommended by Stevo Stevic Part-metric-related PMR inequality chains are elegant and are useful in the study of difference equations. In this paper, we establish a new PMR inequality chain, which is then applied to show the global asymptotic stability of a class of rational difference equations.

A new nonlinear sum-difference inequality in two variables which generalize some existing results and can be used as handy tools in the analysis of certain partial difference equation is discussed. An example to show boundedness of solutions of a difference value problem is also given. Keywords—Sum-Difference inequality, Nonlinear, Boundedness.

Some new criteria for the oscillation of certain difference equations with mixed nonlinearities are established. The main tool in the proofs is an inequality due to Hardy, Littlewood, and Pólya. c © 2006 Elsevier Ltd. All rights reserved.

We establish a general form of sum-difference inequality in two variables, which includes both two distinct nonlinear sums without an assumption of monotonicity and a nonconstant term outside the sums. We employ a technique of monotonization and use a property of stronger monotonicity to give an estimate for the unknown function. Our result enables us to solve those discrete inequalities consid...