Ozaki-Type Bi-Close-to-Convex and Bi-Concave Functions Involving a Modified Caputo’s Fractional Operator Linked with a Three-Leaf Function

Abstract

The focus of the present work is on the establishment and investigation of the coefficient estimates of two new subclasses of bi-close-to-convex functions and bi-concave functions; these are of an Ozaki type and involve a modified Caputo’s fractional operator that is associated with three-leaf functions in the open unit disc. The classes are defined using the notion of subordination based on the previously established fractional integral operators and classes of starlike functions associated with a three-leaf function. For functions in these classes, the Fekete-Szegö inequalities and the initial coefficients, |a2| and |a3|, are discussed. Several new implications of the findings are also highlighted as corollaries.

Keywords

• analytic function
• univalent function
• bi-univalent function
• bi-starlike and bi-convex function
• coefficient bounds
• convolution