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In this paper, we discuss and introduce a new study using an integral operator w k , μ m in geometric function theory, especially sandwich theorems. We obtained some conclusions for differential subordination and superordination for a new formula generalized integral operator. In addition, certain sandwich theorems were found. The differential subordination theory's features and outcomes are symmetric to those derived using the differential subordination theory. [ABSTRACT FROM AUTHOR]

We present several new results for higher-order (fourth-order) differential subordination and superordination in this paper by using the new operator Hα,β,δ,ξ,γ,nf(v) and offer numerous new findings for fourth-order differential subordination and superordination. The innovative discoveries presented here are connected to those mentioned in previous articles. The differential subordination theory's characteristics and outcomes are symmetric to the properties gained. Sandwich-type theorems are created by merging differential superordination theory with sandwich-type theorems. [ABSTRACT FROM AUTHOR]

This paper is concerned with studying some results by introducing a new Hadamard product M γ , b , v , δ C , η operator for differential subordination and superordination for certain univalent functions in the open unit disc U. Firstly, we state some basic definitions and required theorems. Furthermore. Some sandwich theorems are derived. The differential subordination theory's features and outcomes are symmetric to those derived using the differential superordination theory. [ABSTRACT FROM AUTHOR]

In this current study, we aim to give some results for third-order differential subordination and superordination for analytic functions in U = { z ∈ ℂ : | z | < 1 }   involving the generalized operator I α , β j f . The results are derived by investigating relevant classes of admissible functions. Some new results on differential subordination and superordination with some sandwich theorems are obtained. Moreover, several particular cases are also noted. The properties and results of the differential subordination are symmetry to the properties of the differential superordination to form the sandwich theorems. [ABSTRACT FROM AUTHOR]

We propose, in the present paper, to derive some differential subordination results. The work is developed in the case of analytic functions defined on the open unit disc. The results will be formulated by making use of an Atangana–Baleanu fractional integral operator and Bessel functions. For the newly obtained theorems, certain interesting consequences are also considered. Univalent function selections with specific symmetry properties were involved. [ABSTRACT FROM AUTHOR]

We present several new results for fourth-order differential subordination and superordination in this paper by using the differential linear operator Γ π , ρ , β , μ f z . Relevant connections between the new results presented here and those considered in previous works are addressed. The properties and results concerning the differential subordination theory are symmetric to the properties obtained using the differential superordination theory, and by combining them, sandwich-type theorems are obtained. [ABSTRACT FROM AUTHOR]

In this research, we study suitable classes of admissible functions and establish the properties of third-order differential subordination by making use a certain differential operator of analytic functions in U and have the normalized Taylor–Maclaurin series of the form: f (z) = z + ∑ n = 2 ∞ a n z n ,   (z ∈ U) . Some new results on differential subordination with some corollaries are obtained. These properties and results are symmetry to the properties of the differential superordination to form the sandwich theorems. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish certain subordination results for analytic functions involving Atangana–Baleanu fractional integral of Bessel functions. Studying subordination properties by using various types of operators is a technique that is widely used. [ABSTRACT FROM AUTHOR]

Both the theory of differential subordination and its dual, the theory of differential superordination, introduced by Professors Miller and Mocanu are based on reinterpreting certain inequalities for real-valued functions for the case of complex-valued functions. Studying subordination and superordination properties using different types of operators is a technique that is still widely used, some studies resulting in sandwich-type theorems as is the case in the present paper. The fractional integral of confluent hypergeometric function is introduced in the paper and certain subordination and superordination results are stated in theorems and corollaries, the study being completed by the statement of a sandwich-type theorem connecting the results obtained by using the two theories. [ABSTRACT FROM AUTHOR]

Since in many particular cases checking directly the conditions from the definitions of starlikeness or convexity of a function can be difficult, in this paper we use the theory of differential subordination and in particular the method of admissible functions in order to determine conditions of starlikeness and convexity for the confluent (Kummer) hypergeometric function of the first kind. Having in mind the results obtained by Miller and Mocanu in 1990 who used a , c ∈ R , for the confluent (Kummer) hypergeometric function, in this investigation a and c complex numbers are used and two criteria for univalence of the investigated function are stated. An example is also included in order to show the relevance of the original results of the paper. [ABSTRACT FROM AUTHOR]