Papers by Abdulmtalb Hussen
Bounding coefficients for certain subclasses of bi-univalent functions related to Lucas-Balancing polynomials
AIMS mathematics, 2024
An Application of the Mittag-Leffler-type Borel Distribution and Gegenbauer Polynomials on a Certain Subclass of Bi-Univalent Functions
Heliyon, May 1, 2024
Mathematics, Dec 12, 2023
In this paper, we introduce a new subclass of bi-univalent functions defined using Lucas-Balancin... more In this paper, we introduce a new subclass of bi-univalent functions defined using Lucas-Balancing polynomials. For functions in each of these bi-univalent function subclasses, we derive estimates for the Taylor-Maclaurin coefficients |a 2 | and |a 3 | and address the Fekete-Szegö functional problems for functions belonging to this new subclass. We demonstrate that several new results can be derived by specializing the parameters in our main findings. The results obtained from this study will enrich the theoretical foundation of this field and open new avenues for mathematical inquiry and application.
International journal of scientific and research publications, Apr 12, 2021
The classical Fejer-Riesz Theorem has many applications in various mathematical fields. This surv... more The classical Fejer-Riesz Theorem has many applications in various mathematical fields. This survey paper presents this theorem in several versions: 1) with operatorvalued functions as coefficients, 2) in 2 × 2 matrix form, and 3) in the multivariate case. The main ideas of the proofs are sketched.
Mathematics
Subclasses of analytic and bi-univalent functions have been extensively improved and utilized for... more Subclasses of analytic and bi-univalent functions have been extensively improved and utilized for estimating the Taylor–Maclaurin coefficients and the Fekete–Szegö functional. In this paper, we consider a certain subclass of normalized analytic and bi-univalent functions. These functions have inverses that possess a bi-univalent analytic continuation to an open unit disk and are associated with orthogonal polynomials; namely, Gegenbauer polynomials that satisfy subordination conditions on the open unit disk. We use this subclass to derive new approximations for the second and third Taylor–Maclaurin coefficients and the Fekete–Szegö functional. Furthermore, we discuss several new results that arise when we specialize the parameters used in our fundamental findings.
Journal of Applied Mathematics and Physics
In this review article, we begin with reviewing Calculus of variations giving few examples on its... more In this review article, we begin with reviewing Calculus of variations giving few examples on its use to solve a large number of problems in geometry, physics, and other branches of knowledge. Afterwards, we direct our attention to different methods of variations which evolved during the last century and which include their use in eigenvalue problems and in finite difference methods and those adopted in classical and quantum mechanics. The methods used in evaluating products and quotients of functionals are also discussed along with variational iteration methods. Later on, a good number of applications in different areas are presented and discussed; then a concluding discussion is given.
International Journal of Scientific and Research Publications (IJSRP), 2021
The classical Fejer-Riesz Theorem has many applications in various mathematical fields. This surv... more The classical Fejer-Riesz Theorem has many applications in various mathematical fields. This survey paper presents this theorem in several versions: 1) with operatorvalued functions as coefficients, 2) in 2 × 2 matrix form, and 3) in the multivariate case. The main ideas of the proofs are sketched.

In data analysis and signal processing, the recovery of structured functions (in terms of frequen... more In data analysis and signal processing, the recovery of structured functions (in terms of frequencies and coefficients) with respect to certain basis functions from the given sampling values is a fundamental problem. The original Prony method is the main tool to solve this problem, which requires the equispaced sampling values. In this dissertation, we use the equispaced sampling values in the frequency domain after the short time Fourier transform in order to reconstruct some signal expansions, such as the exponential expansions and the cosine expansions. In particular, we consider the case that the phase of the cosine expansion is quadratic. Moreover, we work on the expansion problem based on the eigenfunctions of some linear operators. In addition, when the signals contain two different models, we develop a method that separate the signals in single-models and then solve the problem. We also consider the situation that when some of the sampling values are corrupted.
Mathematical and Computational Applications
In data analysis and signal processing, the recovery of structured functions from the given sampl... more In data analysis and signal processing, the recovery of structured functions from the given sampling values is a fundamental problem. Many methods generalized from the Prony method have been developed to solve this problem; however, the current research mainly deals with the functions represented in sparse expansions using a single generating function. In this paper, we generalize the Prony method to solve the sparse expansion problem for two generating functions, so that more types of functions can be recovered by Prony-type methods. The two-generator sparse expansion problem has some special properties. For example, the two sets of frequencies need to be separated from the zeros of the Prony polynomial. We propose a two-stage least-square detection method to solve this problem effectively.
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Papers by Abdulmtalb Hussen