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This article aims to significantly advance geometric function theory by providing a valuable contribution to analytic and multivalent functions. It focuses on differential subordination and superordination, which characterize the interactions between analytic functions. To achieve our goal, we employ a method that relies on the characteristics of differential subordination and superordination. As one of the latest advancements in this field, this technique is able to derive several results about differential subordination and superordination for multivalent functions defined by the new operator M λ , p m v , ρ ; η F ξ within the open unit disk A . Additionally, by employing the technique, the differential sandwich outcome is achieved. Therefore, this work presents crucial exceptional instances that follow the results. The findings of this paper can be applied to a wide range of mathematical and engineering problems, including system identification, orthogonal polynomials, fluid dynamics, signal processing, antenna technology, and approximation theory. Furthermore, this work significantly advances the knowledge and understanding of the analytical functions of the unit and its interactive higher relations. The characteristics and consequences of differential subordination theory are symmetric to those of differential superordination theory. By combining them, sandwich-type theorems can be derived. [ABSTRACT FROM AUTHOR]

In the current paper, we define some subclasses of holomorphic functions in the open disk u that are defined by the differential operator. These subclasses are defined in the open disk u. We make some estimates for the bounds of the Fekete-Szego inequality as well as the coefficients | a2 | and | a3 | for functions that belong to these subclasses. Also, some of the results of these subclasses have been generalized, particularly those that involve the majorization and quasi-subordination concepts. [ABSTRACT FROM AUTHOR]

In this paper we give the best form of a strongly starlikeness condition. Some consequences of this result are deduced. The basic tool of the research is the method of differential subordinations.

In this paper, we use the use the linear operator Ⳅ,σ x(u, v, y)f(z) and the concept of the subordination to analyse the general class of all analytic univalent functions. Our main results are implication properties between the classes of such functions and the application of these properties to special cases. [ABSTRACT FROM AUTHOR]

Copyright of Baghdad Science Journal is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we introduce and study certain subclass of meromorphic univalent functions by using a linear operator by means of a Hadamard product involving some suitably normalized meromorphically q-Hypergeometric functions, in the punctured open unit disk. Some properties like, coefficients inequalities, growth and distortion theorems, closure theorems, Extreme Points and Radii of meromorphic starlikeness and meromorphic convexity are obtained. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to study some subclasses of analytic and bi-univalent functions which are defined in the open unit disk and associated with Gegenbauer polynomials. Coefficient bounds and Fekete-Szego inequalities for functions belonging to these subclasses are established. [ABSTRACT FROM AUTHOR]

Copyright of Baghdad Science Journal is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In the present paper, the authors introduce and investigate two new subclasses,namely and of the class 𝜅-fold biunivalent functions in the open unit disk . The initial coefficients for all of the functions that belong to them are determined, as well as the coefficients for functions that belong to a field determining these coefficients are also determined which require a complicated process. The bounds for the initial coefficients and that contained among the remaining results in our analysis are obtained. In addition, some specific special improver results for the related classes are provided. [ABSTRACT FROM AUTHOR]

Copyright of Al-Mustansiriyah Journal of Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)