Subordination results for some subclasses of analytic functions

El-Ashwah, R. M.; Aouf, M. K.; Shamandy, A.; Ali, Ekram E.

doi:10.21136/mb.2011.141652

Cited by 13 publications

(14 citation statements)

References 19 publications

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“…There is still an obvious problem for |𝑎 𝑛 |, 𝑛 ∈ ℕ − {1, 2, 3}, where ℕ = {1, 2, 3, … }. El-Ashwah and Thomas [7] acquainted the family 𝑆 𝑠𝑐 * of functions named starlike in the sense of symmetric conjugate points, they are the functions 𝑠 ∈ 𝑆 provide the inequality…”

Section: Sigmamentioning

confidence: 99%

Quasi subordinations for bi-univalent functions with symmetric conjugate points

SAKAR

2024

Sigma J Eng Nat Sci - Sigma Müh Fen Bil Derg

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Many researchers have recently acquainted and researched several interesting subfamilies of bi-univalent function family 𝛿 and they have found non-sharp estimates on the first two Taylor-Maclaurin coefficients |𝑎 2 | and |𝑎 3 |. In this current work, the subfamily ℱ 𝛿,𝑞 𝑠𝑐 (𝛼, Ξ) of bi-univalent functions in the sense of symmetric conjugate points with quasi subordination is defined. The Maclaurin coefficients |𝑎 2 |, |𝑎 3 | and besides related with these coefficients |𝑎 3 − 𝑎 2 2 | for functions belonging to this subfamily are derived. Further some corollaries are also presented.

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Section: Sigmamentioning

confidence: 99%

Quasi subordinations for bi-univalent functions with symmetric conjugate points

SAKAR

2024

Sigma J Eng Nat Sci - Sigma Müh Fen Bil Derg

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“…where K and L are given by (32), and taking the absolute value of (35), from (14), we obtain the inequality (31). The proof is complete.…”

Section: Corollarymentioning

confidence: 99%

“…El-Ashwah and Thomas [14] introduced the class S * sc of starlike with respect to symmetric conjugate points as follows:…”

Section: Introductionmentioning

confidence: 99%

Coefficient Estimates for the Functions with Respect to Symmetric Conjugate Points Connected with the Combination Binomial Series and Babalola Operator and Lucas Polynomials

El-Deeb

Lupaş

2022

Fractal Fract

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By using Lucas polynomials, we define a new subclass of analytic bi-univalent functions, class Σ, in the open unit disc with respect to symmetric conjugate points connected with the combination Binomial series and Babalola operator. The bounds on the initial coefficients a2 and a3 for the functions in this new subclass of Σ are investigated. Moreover, we obtain an estimation for the Fekete–Szego problem for the function subclass defined in this paper. Relevant connections of these results are presented here as corollaries.

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“…Jackson [1,2] discovered the most crucial step in q-calculus and established the useful formulas for q-integral and q-derivative operators. Its applications in fields such as regular fractional calculus, including combinatorics, orthogonal polynomials and fundamental hypergeometric functions, have generated many studies (see, for example, [3][4][5][6] and others).…”

Section: Introductionmentioning

confidence: 99%