On Some Sandwich Results of Univalent Functions Related by Differential Operator

Abstract

Th goal of the pr s nt p p r is to obt in some differ tial sub rdin tion an sup r dination the rems for univalent functions related b differential operator Also, we discussed some sandwich-type results.

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).…”

Sandwich Subordinations Imposed by New Generalized Koebe-Type Operator on Holomorphic Function Class

“…In effect, interesting recent studies have emanated about dealing with subordinate and superordinate techniques and sandwiches problems correlated with numerous complex operators, for instance, Atshan et al [17], Sokół et al [18], Zayed and Bulboacă [19], Al-Janaby and Ahmad [20], Mishra and Soren [21], Al-Janaby and Darus [22], Al-Janaby et al ( [23], [24]), Ghanim and Al-Janaby ( [25], [26]), Attiy ([27], [28]), Lupaş and Oros [29] and Atshan ( [30], [31]).…”

Third-Order Differential Subordination and Superordination Results for Analytic Univalent Functions Using Hadamard Product Operator

“…The recent work on differential subordination by some authors [4,8,12,16,15,17,19,21,23,24,25,26,27] drew attention from many experts in this area. see ( [1,2,3,5,6,7,9,10,11,13,14,18,22]).…”