Study on Properties of Monotone Function
Journal Title: Scholars Journal of Physics, Mathematics and Statistics - Year 2015, Vol 2, Issue 2
Abstract
Firstly, this paper gives the conditions of the existence of four kinds of unilateral limits and limit values for monotone function; points out the relationship between the existence of four kinds of unilateral limits and sequence limit, and weakens the conditions of Heine theorem. Secondly, it demonstrates that the discontinuity points of monotone functions are the discontinuity points of the first kind, and their number is countable at most within a interval. Finally, it gives the relationship between upper and lower limits of bounded sequence and monotone function and bounded sequence, and provides corresponding application examples.
Authors and Affiliations
Caixia Zhang
Keywords
Related Articles
- EP ID EP384445
- DOI -
- Views 78
- Downloads 0
One-Sided Generalized Likelihood Ratio Test for Normal Population Mean Value
Generalized likelihood ratio test (GLRT) is a very important method of hypothesis testing in mathematical statistics, which is widely applied. In this paper, GLRT is used to deduce the rejection region of hypothesis test...
Calibration of Pipeline Friction Coefficient Based on Random Optimization
The changed friction resistance coefficient of the pipeline after the oilfield water injection pipe network system is used for a long term cannot reflect the actual conditions of the pipeline accurately. As the main para...
Existence of positive solutions for boundary value problems for a class of nonlinear high-order differential equation
In this paper, we investigate a kind of boundary value problem of nonlinear high-order differential equation. Making use of the fixed point theorems on cone and by constructing the correction function, we obtain the exis...
Fabrication of Schottky Barrier Solar Cells of Copper (I) Oxide (Cu2O) by the Process of Partial Thermal Oxidation
Copper (1) Oxide (Cu2O) is a non-stoichiometric semi-conductor. It is envisaged that this semiconductor could be used for the fabrication of low-cost solar cells. These solar cells have been fabricated by researchers usi...
Homogeneous Bi-Quadratic Equation with Four Unknowns
We obtain infinitely many non-zero integer quadruples satisfying the the Biquadratic equation with four unknowns. Various interesting properties among the values of x, y, z and w are presented.