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Papers by Mirzaolim Turabaev

Research paper thumbnail of Fekete-Szegö problem for a new subclass of analytic functions satisfyingsubordinate condition associated with Chebyshev polynomials

TURKISH JOURNAL OF MATHEMATICS, 2021

In this paper,we define a class of analytic functions F (β,λ) (H, α, δ, µ) , satisfying the follo... more In this paper,we define a class of analytic functions F (β,λ) (H, α, δ, µ) , satisfying the following subordinate condition associated with Chebyshev polynomials    α [ zG ′ (z) G (z) ] δ + (1 − α) [ zG ′ (z) G (z) ] µ [ 1 + zG ′′ (z) G ′ (z) ] 1−µ    ≺ H (z, t) , where G (z) = λβz 2 f ′′ (z) + (λ − β) zf ′ (z) + (1 − λ + β) f (z) , 0 ≤ α ≤ 1, 1 ≤ δ ≤ 2, 0 ≤ µ ≤ 1, 0 ≤ β ≤ λ ≤ 1 and t ∈ (1 2 , 1 ]. We obtain initial coefficients |a2| and |a3| for this subclass by means of Chebyshev polynomials expansions of analytic functions in D. Furthermore, we solve Fekete-Szegö problem for functions in this subclass.We also provide relevant connections of our results with those considered in earlier investigations. The results presented in this paper improve the earlier investigations.

Research paper thumbnail of Some results on two new subclasses of p-valent spirallike and convexlike functions

New Trends in Mathematical Science, 2019

In the present paper, we introduce two new subclasses of p-valent spirallike and p-valent convexl... more In the present paper, we introduce two new subclasses of p-valent spirallike and p-valent convexlike functions which are analytic in the open unit disk. We prove necessary and sufficient conditions for this newly defined classes and also point out some known consequences of our results.

Research paper thumbnail of Fekete-Szegö problem for a new subclass of analytic functions satisfyingsubordinate condition associated with Chebyshev polynomials

TURKISH JOURNAL OF MATHEMATICS, 2021

In this paper,we define a class of analytic functions F (β,λ) (H, α, δ, µ) , satisfying the follo... more In this paper,we define a class of analytic functions F (β,λ) (H, α, δ, µ) , satisfying the following subordinate condition associated with Chebyshev polynomials    α [ zG ′ (z) G (z) ] δ + (1 − α) [ zG ′ (z) G (z) ] µ [ 1 + zG ′′ (z) G ′ (z) ] 1−µ    ≺ H (z, t) , where G (z) = λβz 2 f ′′ (z) + (λ − β) zf ′ (z) + (1 − λ + β) f (z) , 0 ≤ α ≤ 1, 1 ≤ δ ≤ 2, 0 ≤ µ ≤ 1, 0 ≤ β ≤ λ ≤ 1 and t ∈ (1 2 , 1 ]. We obtain initial coefficients |a2| and |a3| for this subclass by means of Chebyshev polynomials expansions of analytic functions in D. Furthermore, we solve Fekete-Szegö problem for functions in this subclass.We also provide relevant connections of our results with those considered in earlier investigations. The results presented in this paper improve the earlier investigations.

Research paper thumbnail of Some results on two new subclasses of p-valent spirallike and convexlike functions

New Trends in Mathematical Science, 2019

In the present paper, we introduce two new subclasses of p-valent spirallike and p-valent convexl... more In the present paper, we introduce two new subclasses of p-valent spirallike and p-valent convexlike functions which are analytic in the open unit disk. We prove necessary and sufficient conditions for this newly defined classes and also point out some known consequences of our results.