Inequalities on the generalized abc index

In this work, we obtained new results relating the generalized atom-bond connectivity index with the general Randić index. Some of these inequalities for ABCα improved, when α=1/2, known results on the ABC index. Moreover, in order to obtain our results, we proved a kind of converse Hölder inequality, which is interesting on its own.This research was supported by a grant from Agencia Estatal de Investigación (PID2019- 106433GBI00/ AEI/10.13039/501100011033), Spain. The research of José M. Rodríguez was supported by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of the Excellence of University Professors (EPUC3M23) and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation