Revised Manuscript On New Sandwich Results of Univalent Functions Defined by a Linear Operator

Abstract

In this research paper, we explain the use of the convexity and the starlikness properties of a given function to generate special properties of differential subordination and superordination functions in the classes of analytic functions that have the form in the unit disk. We also show the significant of these properties to derive sandwich results when the Srivastava- Attiya operator is used.

New Sandwich-Type Results of Meromorphic Multivalent Functions Defined by Rafid operator

“…Through the utilisation of conclusions, (see [2,4,5,6,9,13,14,18,20,22,23,24,25]) to fulfil necessary conditions for satisfying of normailzed analytic functions…”

“…For every 𝓅(𝓏) that fulfil equation (1.3), a univalent dominating function 𝓆 ̌(𝓏) that fulfils 𝑞 ̌(𝓏) ≺ 𝓆(𝓏) for every dominent 𝓆(𝓏) of (1.3) it's claimed to obtain best dominent. Millier, Mocaanu [16] and more authors [1,2,3,4,5,6,7,8,9,10,12] and also [13,14,18,20,21,24,25] established necessary conditions on the functions 𝔜, 𝓅, and 𝔛 in order to obtain the following conclusion: 𝔜(𝓏) ≺ 𝔛(𝓅(𝓏), 𝓏𝓅 ′ (𝓏), 𝓏 2 𝓅 ′′ (𝓏); 𝓏) → 𝓆(𝓏) ≺ 𝓅(𝓏)(𝓏 ∈ 𝔘).…”

Differential Subordination and Superordination Using an Integral Operator for Certain Subclasses of p-Valent Functions

“…The subordination and superordination features were investigated by Lupas and Oros [8] in 2021 by the utilization of the fractional integral of the confluent hypergeometric function. In the year 2022, other authors conducted investigations pertaining to subordination and its associated qualities [12][13][14].…”

On Sandwich Results of Meromorphic Multivalent Functions Defined by a New Hadamard Product Operator

“…Miller and Mocanu [17] and other authors [1,2,3,4,5,6,7,8,9,10,13] and also [14,15,18,19,20,23,24] discovered sufficient conditions for the functions ℎ, 𝑝, and 𝜙 for which the following result: ℎ(𝑧) ≺ 𝛶(𝑝(𝑧), 𝑧𝑝 ′ (𝑧), 𝑧 2 𝑝 ′′ (𝑧); 𝑧) ⇒ 𝑞(𝑧) ≺ 𝑝(𝑧)(𝑧 ∈ 𝑈).…”

“…Using the results, (see [1,2,4,5,6,7,14,15,18,19,21,22,23,24]) to obtain adequate criteria for the satisfaction of normalized analytic functions…”