Open Journal of Mathematical Analysis (OMA)

The Open Journal of Mathematical Analysis (OMA) ISSN: 2616-8103 (Print), 2616-8111(Online) is an international research journal dedicated to the publication of original and high quality research papers that treat the mathematical analysis in broad and abstract settings. To ensure fast publication, editorial decisions on acceptance or otherwise are taken within 4 to 12 weeks (three months) of receipt of the paper.

Accepted articles are immediately published online as soon as they are ready for publication. There is one volume containing two issues per year. The issues will be finalized in June and December of every year. The printed version will be published in December of every year. The journal will also publish survey articles giving details of research progress made during the last three decades in a particular area.

Latest Published Articles

Author(s): Christophe Chesneau1
1Department of Mathematics, LMNO, University of Caen-Normandie, 14032 Caen, France
Abstract:

In this article, we establish new integral inequalities involving sub-multiplicative functions. We first derive several inequalities of primitive type, followed by new inequalities of the convolution product type. We also obtain integral bounds for functions evaluated on the product of two variables. Finally, we study double integral inequalities and their variations. Simple examples are used to illustrate the theory. The understanding of integral inequalities under submultiplicative assumptions is thus deepened, and some new ideas for further research in mathematical analysis are provided.

Author(s): Abubker Ahmed1,2
1University of Science and Technology, College of Engineering (Sudan)
2Al Mughtaribeen University, College of Engineering, Department of General Sciences (Sudan)
Abstract:

The current study focuses on the investigation and develop of a new approach called Hussein–Jassim method (HJM), suggested lately by Hassan et al.; specifically, we investigate its applicability to fractional ordinary delay differential equations in the Caputo fractional sense. Several examples are offered to demonstrate the method’s reliability. The results of this study demonstrate that the proposed method is highly effective and convenient for solving fractional delay differential equations.

Author(s): Fethi Soltani1,2
1Faculté des Sciences de Tunis, Laboratoire d’Analyse Mathématique et Applications, LR11ES11, Université de Tunis El Manar, Tunis 2092, Tunisia
2Ecole Nationale d’Ingénieurs de Carthage, Université de Carthage, Tunis 2035, Tunisia
Abstract:

We define and study the Stockwell transform \(\mathscr{S}_g\) associated with the Whittaker operator
\[\Delta_{\alpha}:=-\frac{1}{4}\left[x^2\frac{\mbox{d}^2}{\mbox{d}x^2}+(x^{-1}+(3-4\alpha)x)\frac{\mbox{d}}{\mbox{d}x}\right],\]
and prove a Plancherel theorem. Moreover, we define the localization operators \(L_{g,\xi}\) associated to this transform. We study the boundedness and compactness of these operators and establish a trace formula. Finally, we give a Shapiro-type uncertainty inequality for the modified Whittaker-Stockwell transform \(\mathscr{S}_g\).

Author(s): Ayotunde Olajide Lasode1, Rasheed Olawale Ayinla2, Risikat Ayodeji Bello2, Atinuke Ayanfe Amao1, Lolade Modupe Fatunsin3, Bitrus Sambo4, Oluwasegun Awoyale5
1Department of Mathematics, University of Ilorin, Ilorin, Nigeria
2Department of Mathematics and Statistics, Kwara State University, Malete, Nigeria
3Department of Mathematics Programme, National Mathematical Centre, Abuja, Nigeria
4Department of Mathematics, Gombe State University, Tudun Wada, Gombe, Nigeria
5Department of Mathematics, Federal College of Education, Kontagora, Niger State, Nigeria
Abstract:

Consider a unit disk \(\Omega=\{z:|z|<1\}\). A large subset of the set of analytic-univalent functions defined in \(\Omega\) is examined in this exploration. This new set contains various subsets of the Yamaguchi and starlike functions, both of which have profound properties in the well-known set of Bazilevič functions. The Ma-Minda function and a few mathematical concepts, including subordination, set theory, infinite series formation and product combination of certain geometric expressions, are used in the definition of the new set. The estimates for the coefficient bounds, the Fekete-Szegö functional with real and complex parameters, and the Hankel determinants with a real parameter are some of the accomplishments. In general, when some parameters are changed within their interval of declarations, the set reduces to a number of recognized sets.

Author(s): Alexander G. Ramm1
1Department of Mathematics, Kansas State University, Manhattan, KS 66506, USA
Abstract:

Let \( u’ + Au = h(u,t) + f(x,t) \) with the initial condition \( u(x,0) = u_0(x) \), where \( u \in H \), \( u’ := u_t := \frac{du}{dt} \), and \( H \) is a Hilbert space. The nonlinear term satisfies the estimate \( \|h(u,t)\| \le a\|u\|^p (1+t)^{-b} \), and the operator \( A \) satisfies the coercivity condition \( (Au,u) \ge \gamma(t)(u,u) \), where \( \gamma(t) = q_0(1+t)^{-q} \). Here, \( a, p, b, q_0, \) and \( q \) are positive constants. Sufficient conditions are established under which the solution exists and is either bounded or tends to zero as \( t \to \infty \).

Author(s): Nader Ali Makboul Hassan1
1Department of Mathematics, Faculty of Education-Hodeidah, University of Hodeidah, PO Box 3114, Hodeidah, Yemen
Abstract:

In this paper, we derive summation formulae for the generalized Legendre-Gould Hopper polynomials (gLeGHP) \({}_SH^{(m)}_n(x,y,z,w)\) and \(\frac{{}_RH^{(m)}_n(x,y,z,w)}{n!}\) by using different analytical means on their respective generating functions. Further, we derive the summation formulae for polynomials related to \({}_SH^{(m)}_n(x,y,z,w)\) and \(\frac{{}_RH^{(m)}_n(x,y,z,w)}{n!}\) as applications of main results. Some concluding remarks are also given.

Author(s): Gurwinder Kaur1, Sukhwinder Singh Billing2, Sukhjit Singh Dhaliwal3
1Department of Mathematics GSSDGS Khalsa College, Patiala-147001, Punjab, India.
2Department of Mathematics Sri Guru Granth Sahib World University Fatehgarh Sahib-140407, Punjab, India.
3Department of Mathematics Sant Longowal Institute of Engineering & Technology Deemed University, Longowal-148106, Punjab, India.
Abstract:

In this paper, the differential subordination \( \frac{b}{\phi(z)}+ c~ \phi(z) + d~ \frac{z \phi'(z)}{\phi^{k}(z)} \prec s(z), k\geq 1, z\in\mathbb{E}\) is studied by using Lowner Chain. The corresponding result for differential superordination is also obtained to get sandwich type result. Consequently, we obtain sufficient conditions for Starlikeness and Convexity of analytic function \(f\).

Author(s): Farid Messelmi1
1Department of Mathematics and LDMM Laboratory, Universite of Djelfa, Algeria.
Abstract:

The purpose of this paper is to apply the concept of \(log -\)series in order to determine the sum of certain power series, where the n-th terms involves the factorial mapping, the generalized harmonic numbers and the reciprocals of factorial sums.

Author(s): Mogoi N. Evans1, Robert Obogi2
1Department of Pure and Applied Mathematics Jaramogi Oginga Odinga University of Science and Technology, Kenya.
2Department of mathematics and actuarial science Kisii University, Kenya.
Abstract:

This paper investigates the geometry and norm-attainability of operators within various operator ideals, with a particular focus on the role of singular values and compactness. We explore the behavior of norm-attainable operators in the context of classical operator ideals, such as trace-class and Hilbert-Schmidt operators, and examine how their geometric and algebraic properties are influenced by membership in these ideals. A key result of this study is the connection between the singular values of trace-class operators and their operator norm, establishing a foundational relationship for understanding norm-attainment. Additionally, we explore the conditions under which weakly compact and compact operators can attain their operator norm, providing further insights into the structural properties that govern norm-attainability in operator theory. The findings contribute to a deeper understanding of the interplay between operator ideals and norm-attainability, with potential applications in functional analysis and related fields.

Author(s): Ahmed Chana1, Abdellatif Akhlidj1, Zakaria Sadik1
1Laboratory of Fundamental and Applied Mathematics, Department of Mathematics and Informatics, Faculty of Sciences Ain Chock, University of Hassan II, B.P 5366 Maarif, Casablanca, Morocco
Abstract:

The primary objective of this paper is to introduce a novel integral transform, referred to as the Hartley-Bessel-Stockwell transform, and to establish several fundamental results associated with it. Specifically, we derive generalized versions of Parseval’s identity, Plancherel’s theorem, the inversion formula, and Calderon’s reproducing formula for this transform. Furthermore, we investigate the concentration properties of the Hartley-Bessel-Stockwell transform on sets of finite measure and present an uncertainty principle for orthonormal sequences. Finally, leveraging the theory of reproducing kernels and best approximation methods, we examine the extremal functions associated with this transform. We provide their integral representations and derive optimal estimates for these functions within weighted Sobolev spaces.