Monotonicity of ratios of q-Kummer confluent hypergeometric and q-hypergeometric functions and associated Tur\'an types inequalities

Abstract

In this paper we prove monotonicity of some ratios of $q$--Kummer confluent hypergeometric and $q$--hypergeometric functions. The results are also closely connected with Tur\'an type inequalities. In order to obtain main results we apply methods developed earlier by the authors for the case of classical Kummer and Gauss hypergeometric functions.