Whether people tend to punish criminals in a socially-optimal manner (i.e., hyperbolic punishment) or not is unknown. By adopting mathematical models of probabilistic punishment behavior (i.e., ...

In this paper, we defined and studied the concept of exponential type multiplicatively convex functions and some of their algebraic properties. We derived Hermite-Hadamard inequalities for this class ...

where a ¹ 0 and b is a constant called the base of the exponential function. b > 0 and b ¹ 1 x is the independent variable. It is the exponent of the constant, b. Thus exponential functions have a ...

A PHASE relation familiar to students of applied mathematics exists between a simple harmonic oscillation and its derivative. Similar relations exist between exponential functions and their ...