Browsing by Author "Shaba, Timilehin Gideon"

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Applications of Q-Derivative Operator to Subclasses of Bi-Univalent Functions Involving Gegenbauer Polynomials
(Taylor & Francis Ltd, 2022) Hu, Qiuxia; Shaba, Timilehin Gideon; Younis, Jihad; Khan, Bilal; Mashwani, Wali Khan; Caglar, Murat
In recent years, using the idea of analytic and bi-univalent functions, many ideas have been developed by different well-known authors, but the using Gegenbauer polynomials along with certain bi-univalent functions is very rare in the literature. We are essentially motivated by this recent research going on, here in our present investigation, we make use of certain q-derivative operator and Gegenbauer polynomials and define a new subclass of analytic and bi-univalent functions. We then obtain certain coefficient bounds, the Fekete-Szego inequalities and upper bounds for the second-order Hankel determinant for the defined functions class.
(P, Q)-Lucas Polynomial Coefficient Relations of Bi-Univalent Functions Defined by the Combination of Opoola and Babalola Differential Operators
(Springer Heidelberg, 2022) Orhan, Halit; Shaba, Timilehin Gideon; Caglar, Murat
In the discipline of geometric function theory, Lucas polynomials and other special polynomials have recently acquired traction. We establish a new class of bi-univalent functions and get coefficient estimates and Fekete-Szego inequalities for this new class in this paper by connecting these polynomials, subordination and combination of Babalola and Opoola operator.
Toeplitz Determinants for Λ- Pseudo-Starlike Functions
(Korean Mathematical Soc, 2024) Caglar, Murat; Ibrahim, Ismaila O.; Shaba, Timilehin Gideon; Wanas, Abbas Kareem
. In this article, by making use of the )-pseudo-starlike functions, we introduce a certain family of normalized analytic functions in the open unit disk U and we establish coefficient estimates for the first four determinants of the Toeplitz matrices T2(2), T2(3), T3(2) and T3(1) for the functions belonging to this family. Further, some known and new results which follow as special cases of our results are also mentioned.