Subordination and superordination preserving properties for a family of integral operators involving the Noor integral operator

Abstract

In the present paper, we introduce a family of integral operators Ip,n,δλ,μ(a,b,c) associate with the Noor integral operator in the open unit disk U={z∈C:|z|<1}, which is defined by the convolution [fp,δμ(a,b,c)(z)](-1)*f(z), where fp,δμ(a,b,c)(z)=(1-μ+δ)zp2F1(a,b;c;z)+(μ-δ)z[zp2F1(a,b;c;z)]′+μδz2[zp2F1(a,b;c;z)]″(p∈N={1,2,⋯};μ,δ⩾0;z∈U). By using the operator Ip,n,δλ,μ(a,b,c), we investigate some subordination and superordination preserving properties for certain classes of analytic and multivalent functions in U. Various sandwich-type results for these multivalent functions are also obtained.

Keywords

• Analytic and multivalent functions
• Hadamard product (or convolution)
• Differential subordination
• Superordination
• Noor integral operator
• Sandwich-type result