Acta mathematica scientia,Series B ›› 2018, Vol. 38 ›› Issue (6): 1751-1758.

• Articles • Previous Articles     Next Articles

HARNACK AND MEAN VALUE INEQUALITIES ON GRAPHS

Yong LIN1, Hongye SONG1,2   

  1. 1 Department of Mathematics, Renmin University of China, Beijing 100872, China;
    2 School of General Education, Beijing International Studies University, Beijing 100024, China
  • Received:2017-08-10 Revised:2018-01-26 Online:2018-12-25 Published:2018-12-28
  • Contact: Hongye SONG E-mail:songhongye@bisu.edu.cn
  • Supported by:
    The authors were supported by the National Science Foundation of China (11671401).

Abstract: We prove a Harnack inequality for positive harmonic functions on graphs which is similar to a classical result of Yau on Riemannian manifolds. Also, we prove a mean value inequality of nonnegative subharmonic functions on graphs.

Key words: harmonic function, subharmonic function, Harnack inequality, mean value inequality, graph

Trendmd