Applications of a new linear operator involving Dziok-Srivastava operator and Bessel function of the first kind

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Abstract
This study introduces a new linear operator constructed from the well-known Dziok–Srivastava linear hypergeometric operator, the Bessel function of the first kind, and convolution. Applying the new operator, a class of functions with positive real part is defined and investigated concerning inclusion relations, the necessary and sufficient conditions for functions to belong to this class, as well as starlikeness and convexity conditions. The properties of the new class to be convex of a certain order, close-to-convex and starlike of a certain order are highlighted and examples are also included to prove that the new outcome is applicable. The methods employed for the investigation are specific to the prolific theory of differential subordination initiated by S.S. Miller and P.T. Mocanu.

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