arXiv subjects

Pshtiwan Othman Mohammed

Publications and source records attributed to Pshtiwan Othman Mohammed.

4 recordsLinked to original sources

arXiv2023

Some $m$-Fold Symmetric Bi-Univalent Function Classes and Their Associated Taylor-Maclaurin Coefficient Bounds

The Ruscheweyh derivative operator is used in this paper to introduce and investigate interesting general subclasses of the function class $Σ_{\mathrm{m}}$ of $m$-fold symmetric bi-univalent analytic functions. Estimates of the initial Taylor-Maclaurin coefficients $\left|a_{m+1}\right|$ and $\left|a_{2 m+1}\right|$ are obtained for functions of the subclasses introduced in this study, and the consequences of the results are discussed. The results presented would generalize and improve on some recent works by many earlier authors. In some cases, our estimates are better than the existing coefficient bounds. Furthermore, within the engineering domain, this paper delves into a series of complex issues related to analytic functions, $m$-fold symmetric univalent functions, and the utilization of the Ruscheweyh derivative operator. These problems encompass a broad spectrum of engineering applications, including the optimization of optical system designs, signal processing for antenna arrays, image compression techniques, and filter design for control systems. The paper underscores the crucial role of these mathematical concepts in addressing practical engineering dilemmas and fine-tuning the performance of various engineering systems. It emphasizes the potential for innovative solutions that can significantly enhance the reliability and effectiveness of engineering applications.

math.CV↗

arXiv2023

Hankel determinant for a general subclass of m-fold symmetric bi-univalent functions defined by Ruscheweyh operator

Making use of the Hankel determinant and the Ruscheweyh derivative, in this work, we consider a general subclass of m-fold symmetric normalized bi-univalent functions defined in the open unit disk. Moreover, we investigate the bounds for the second Hankel determinant of this class and some consequences of the results are presented. In addition, to demonstrate the accuracy on some functions and conditions, most general programs are written in Python V.3.8.8 (2021).

math.CV↗

arXiv2022

On discrete generalized nabla fractional sums and differences

This article investigates a class of discrete nabla fractional operators by using the discrete nabla convolution theorem. Inspired by this, we define the discrete generalized nabla fractional sum and differences of Riemann-Liouville and Caputo types. In the process, we give a relationship between the generalized discrete delta fractional operators introduced by Ferreira \cite{Ferreira} and the proposed discrete generalized nabla fractional operators via the dual identities. Also, we present some test examples to justify the relationship. Moreover, we prove the fundamental theorem of calculus for the defined discrete generalized nabla fractional operators. Inspired by the above operators, we define discrete generalized nabla Atangana-Baleanu-like (or Caputo-Fabrizio-like) fractional sum and differences at the end of the article.

math.CA↗

arXiv2020

Fractional integral inequalities of Hermite-Hadamard type for convex functions with respect to a monotone function

In the literature, the left-side of Hermite--Hadamard's inequality is called a midpoint type inequality. In this article, we obtain new integral inequalities of midpoint type for Riemann--Liouville fractional integrals of convex functions with respect to increasing functions. The resulting inequalities generalize some recent classical integral inequalities and Riemann--Liouville fractional integral inequalities established in earlier works. Finally, applications of our work are demonstrated via the known special functions of real numbers.

math.GM↗