Some Inequalities for Certain <i>p</i>-Valent Functions Connected with the Combination Binomial Series and Confluent Hypergeometric Function

Abstract

The present paper deals with a new differential operator denoted by Fp,tδ,n,b,c,m,β, whose certain properties are deduced by using well-known earlier studies regarding differential inequalities and the Caratheodory function. The new introduced operator is defined by making use of a linear combination of the binomial series and confluent hypergeometric function. In addition, by using special values of the parameters, we establish certain results concretized in specific corollaries, which provide useful inequalities. Studying these properties by using various types of operators is a technique that is widely used.

Keywords

• <i>p</i>-valent
• confluent hypergeometric function
• binomial series