Some Functional Inequalities for Generalized Error Function

摘要

In the paper, the authors present some functional inequalities for the generalized error function. Concretely speaking, the authors present several inequalities of the generalized error function in terms of the arithmetic, logarithmic, and exponential means, find monotonicity, convexity, and concavity of the generalized error function, and, consequently, derive two Grünbaum type and Turán type inequalities.