The problem of iterative roots for strictly monotone self-mappings has been well solved. Most of known results concerning existence of iterative roots for a continuous function were given under the assumption that the function has finitely many non-monotonic points. When a function has infinitely many non-monotonic points, the problem of the existence of its iterative roots will become more com...

Abstract Eroders are monotonic cellular automata with a linearly ordered state set that eventually wipe out any finite island of nonzero states. One-dimensional eroders were studied by Gal’perin in the 1970s, who presented simple combinatorial characterization class. The multi-dimensional case has been Toom and others, but no such found. We prove similar for those one-dimensional even presence ...

In this paper, some logarithmically completely monotonic, strongly completely monotonic and completely monotonic functions related to the gamma, digamma and polygamma functions are established. Several inequalities, whose bounds are best possible, are obtained.