(untitled) (Baghdad Science Journal, 2024)
Previously, many works dealt with the study of the order differential subordination and shortly after that other studies dealt with the order differential subordination in the unit disc. Recently the order differential subordination was presented by Antonino and Miller (2011). This paper looks at a considerably broader class of order differential inequalities and subordination. The authors define the criteria on an admissible class of operators, implying that order differentiale subordination exists. Meromorphic in is a function that is holomorphic in domain except for poles. If it simply states the function is meromorphic. Meromorphic functions in are those that may be represented as a quotient of two entire functions. Struve functions have applications in surface wave and water wave issues, unstable aerodynamics, optical direction and resistive MHD instability theory. Struve functions have lately appeared in a number of particle systems. The idea of differential subordination in is a generalization of differential inequality in , and it was initiated in 1981 by the works of Miller, Mocanu and Reade. In this artical, appropriate classes of admissible functions are examined and the properties of order differential subordination are established by using the operator of meromorphic multivalent functions connected with generalized Struve function. In this study, there is a need to present many concepts including subordination, superordination, the dominant, the best dominant, convolution (or Hadamard product), meromorphic multivalent function, the Struve function addition to the concept of shifted factorial (or Pochhammer symbol) and admissible functions.