On Certain Sufficiency Criteria for p‐Valent Meromorphic Spiralike Functions

Abstract

We consider some subclasses of meromorphic multivalent functions and obtain certain simple sufficiency criteria for the functions belonging to these classes. We also study the mapping properties of these classes under an integral operator.

New Criteria for Meromorphic Multivalent Alpha-Convex Functions

“…And therefore ( ) ∈ ΣM ( , , , ). By taking = 0 and = 1 in Theorem 3, we obtain Corollaries 4 and 5, respectively, proved by Arif [12].…”

“…2 Journal of Applied Mathematics For = 0 and = 1 in (4), we obtain the classes ΣNC ( , , ) and ΣNS ( , , ) of Σ ( ), respectively, studied by Arif [12]; also see [13,14].…”

Sufficiency Criterion for A Subfamily of Meromorphic Multivalent Functions of Reciprocal Order with Respect to Symmetric Points

“…For detail of the related topics, see the work of Al-Amiri and Mocanu [3], Rosihan and Ravichandran [4], Aouf and Hossen [5], Arif [6], Goyal and Prajapat [7], Joshi and Srivastava [8], Liu and Srivastava [9], Raina and Srivastava [10], Sun et al [11], Shi et al [12] and Owa et al [13], see also [14][15][16].…”

Coefficient Inequalities for a Subclass ofp-Valent Analytic Functions

“…By giving specific values to α , β , λ , p , b , and δ in 𝒱𝒟 p λ ( δ , b , α , β ), we obtain many important subclasses studied by various authors in earlier papers; see for details [ 3 – 6 ]; we list some of them as follows: 𝒱𝒟 1 λ (0,2, 0,0) ≡ 𝒮 λ * and 𝒱𝒟 1 λ (1,1, 0,0) ≡ 𝒦 λ , studied by Spacek [ 7 ] and Robertson [ 8 ], respectively; for the advancement work see [ 9 – 11 ]; 𝒱𝒟 1 0 (0,2, α , β ) ≡ 𝒮𝒟 ( α , β ) and 𝒱𝒟 1 0 (1,1, α , β ) ≡ 𝒦𝒟 ( α , β ), studied by both Owa et al and Shams et al [ 12 , 13 ]; 𝒱𝒟 1 λ (0,2, 1,0) ≡ 𝒰𝒮𝒫 ( λ ) and 𝒱𝒟 1 λ (1,1, 1,0) ≡ 𝒰𝒞𝒮𝒫 ( λ ), introduced by Ravichandran et al [ 14 ]; 𝒱𝒟 1 0 ( δ , b , α , β ) ≡ 𝒱𝒟 ( δ , b , α , β ), considered by Latha [ 15 ]; 𝒱𝒟 1 0 (0,2, 0, β ) ≡ 𝒮 *( β ) and 𝒱𝒟 1 0 (1,1, 0, β ) ≡ 𝒦 ( β ), the well-known classes of starlike and convex functions of order β . From the above special cases we note that this class provides a continuous passage from the class of starlike functions to the class of convex functions.…”

“…𝒱𝒟 1 λ (0,2, 0,0) ≡ 𝒮 λ * and 𝒱𝒟 1 λ (1,1, 0,0) ≡ 𝒦 λ , studied by Spacek [ 7 ] and Robertson [ 8 ], respectively; for the advancement work see [ 9 – 11 ];…”