Mathematical Analysis and its Contemporary Applications
Mathematical Analysis and its Contemporary Applications (MACA) is a peer-reviewed, open-access, quarterly journal dedicated to publishing original and high-quality research in classical and modern analysis. Its primary purpose is to explore the mathematical treatment of problems arising in various scientific and engineering disciplines, such as physics, chemistry, and biology . The journal's scope is comprehensive, covering key areas like: Functional Analysis, Real and Harmonic Analysis, Complex Analysis Numerical Analysis, Partial Differential Equations, Dynamical Systems Nonlinear Analysis, Inequalities, Optimization, Control Theory Analytic Number Theory Mathematics in Machine Learning and Data Mining Machine Learning & Functional Analysis Scientific Machine Learning Physics-Informed Machine Learning MACA emphasizes papers that present novel problems and their solutions, with a strong focus on analytical aspects . The journal is committed to a fair and rigorous peer-review process, evaluating submissions solely on scientific merit
Almost convex-valued perturbation to second order sweeping process
This paper deals with nonconvex set-valued perturbation to second order nonlinear evolution system governed by the so-called nonconvex sweeping process for a class of subsmooth moving sets depending on state and velocity. Making use of our recent paper obtained for a convex valued perturbation, we prove a new existence result when the perturbations are almost convex. Furthermore, we apply our result in the study of an optimal control problem known as a minimum time problem.
Copyright (c) 2023 Doria Affane; Mustapha Fateh Yarou
Corrigendum to "Some analytical properties of the hyperbolic sine integral"
We correct an error in Theorem 2.5 of the paper "Some analytical properties of the hyperbolic sine integral" [Mathematical Analysis and its Contemporary Applications, 6(1)(2024), 1-14]. This correction does not affect other results of the paper.
Time-frequency analysis associated with the Hartley-Wigner localization operators
The main crux of this paper is to introduce a new integral transform called the Hartley-Wigner transform and to give some new results related to this transform. Next, we introduce a new class of pseudo-differential operator Lψ1,ψ2(σ) called localization operator which depends on a symbol σ and two admissible functions ψ1 and ψ2, we give criteria in terms of the symbol σ for its boundedness and compactness, we also show that these operators belong to the Schatten-Von Neumann class Sp for all p ∈[1, +∞] and we give a trace formula.
Copyright (c) 2025 Ahmed Chana; Abdellatif Akhlidj
Some fixed point results on weighted rectangular b-metric spaces
In this paper, we prove some fixed point theorems for Reich contraction, Fisher contraction and Chatterjee contraction in the setting of rectangular b-metric spaces by relaxing the rectangular inequality to include unequal weights. Some examples are given which illustrate the newly proven results.
Copyright (c) 2025 Mashkhas M. Hussein; Anter A. Alsayad; Waleed Mohammad Alfaqih
Decomposition of frames in Banach spaces
In this paper, the decomposition of the retro Banach frame (RBF) and operator Banach frame (OBF) into two infinite subsequences has been discussed. In the sequel, we further decompose OBFs into Block sequences and construct OBFs. We demonstrate a result regarding the image of an OBF by a bounded linear operator is also an OBF. Moreover, results related to the perturbation and stability of OBFs have been proved. In the end, we deal with the problem related to the Feichtinger Conjecture as an application.
Orthogonal projections approach to characterization of numerical ranges of elementary operators
Properties of elementary operators have been characterized over the years for instance numerical ranges the operators are implemented by other different types of operators. However, elementary operators implemented by orthogonal projections have not been characterized in terms of numerical ranges. In this paper, we characterize elementary operators in terms of numerical ranges, when they are implemented by orthogonal projections. The results show that the numerical range of a basic elementary operator satisfies the ellipsoidicity criterion. Moreover, the numerical range of a Jordan elementary operator satisfies the spheroidicity criterion.
Copyright (c) 2025 Otae Kelvin Odindo; Benard Okelo; Priscah Omoke
A study on Fekete-Szegö inequality for a class of analytic functions satisfying subordinate conditions associated with Chebyshev polynomials
We define a class of analytic functions, A(H, n, m, λ), satisfying the following condition Dn+m λ f(z) Dn λf(z) ≺H(z, t), where λ ≥0, n, m ∈N∗= N∪{0}, t ∈ 1 2, 1 and for all z ∈Ω. In this study, firstly give estimates for coefficients |a2| and |a3| of functions belong to this class. Furthermore, the Fekete- Szeg¨o inequality was examined for the functions belonging to this class.
Geometry of norm attainability in Orlicz spaces
This paper investigates norm attainability and modular properties in Orlicz spaces, which generalize Lp-spaces and are key in functional analysis and nonlinear problems. It presents theorems on norm attainment, orthogonality, weak compactness, and uniform convexity, and introduces a novel criterion connecting the convexity of the Orlicz function with the smoothness and reflexivity of the space. The research extends classical concepts such as the ∆2-condition to ensure completeness and separability. The results have practical applications in nonlinear optimization, variational analysis, machine learning, signal processing, image reconstruction, and solving PDEs with nonlinear boundary conditions, providing a strong foundation for future research in these areas.
Copyright (c) 2025 Mogoi N. Evans; Robert Obogi
Common fixed point theorem involving contractive conditions of rational type in dislocated quasi-metric space
In this paper, we have proved the existence and uniqueness of a common fixed-point theorem for a finite family of self-mappings involving contractive conditions of Rational type in dislocated quasi-metric spaces by extending and generalizing the result of Jira et al. [10].
On close-to-convex infinitesimal generators with fixed initial coefficient
This article extends the subclasses of infinitesimal generators to Cn,b(alpha) and SS*n,b(alpha) that are associated with close-to-convex and starlike functions with fixed second coefficient. The main result of this study is a solution to an open problem in a certain specific case.
*-woven frames of multipliers in Hilbert C*-modules
In the current article, by using the sequence of adjointable operators from a C*-algebra A into Hilbert A-module H, the *-woven frames of multipliers in Hilbert C*-modules are introduced. Applying invertible elements in L(H), the set of all bounded A-module maps from H into itself, and co-isometry mappings, some new *-woven frames of multipliers in Hilbert A-module H are constructed. Moreover, a woven frame of multipliers in A as a Hilbert C*-module is indicated.
The study of cases of fixed points of a complex function depending on the inputs and concluding examples of useful functions
This work aims to propose mathematical procedures that help to deduce the fixed points of a complex function. These fixed points can also be used as a basis to generate new useful complex functions that have for sure at least one fixed point. Hence, this is a good article for specialists in calculus and analysis and even for beginners in mathematics who want to improve their skills in the field of complex numbers.
Hat functions operational matrix for solving the nonlinear fractional-order integro-differential equation
This paper aims to construct a general formulation for the hat basis functions of the fractional integral operator. We derive the hat basis functions operational matrix of the fractional order integration, and use it to solve the fractional-order integro-differential equation. The method is described and illustrated with a numerical example. The results show that the method is accurate and easy to apply.
Uncertainty principles and extremal functions for generalized Hartley-Gabor transform
The main crux of this paper is to introduce a new integral transform called the generalized Hartley-Gabor transform which generalizes the classical Gabor Fourier transform and to give some new results related to this transform as Plancherel's, Parseval's, inversion and Calderon's reproducing formulas. Next, we analyse the concentration of this transform on sets of finite measures and we give the uncertainty principle for orthonormal sequences. Last, using the best approximations and the theory of reproducing kernels, we study the extremal functions related to this transform and we give an integral representation, band estimates of these functions on weighted Sobolev spaces.
RN-nearly mixed type A-Q functional equation
In this paper, using direct and fixed point methods, we prove the generalized Hyers-Ulam stability of the following mixed additive-quadratic functional equation: 2f((x+y)/2)+2f((x−y)/2)=1/2{(3f(x)−f(−x))+(f(y)+f(−y))} in random normed spaces.
Lie group analysis of partial differential equation with mixed double fractional derivative
Recently, the theory of Lie symmetry group has been extended to some time-fractional partial differential equations with the mixed derivative of Riemann-Liouville time-fractional derivative and integer-order x-derivative. This paper is the first to apply the Lie group method to fractional-order partial differential equations with time-space mixed derivatives. It discusses the Lie symmetry of this nonlinear partial differential equation and obtains the exact solutions of the equation.
fractional partial differential equations
Orthogonality of algebraic elementary operators when their numerical ranges are spheroidal
Characterizations involving algebraic elementary operators have been done over the years, for instance, orthogonality when the operators are induced by other different types of transformations. In particular, algebraic elementary operators induced by norm-attainable maps have not been characterized in terms of orthogonality when their numerical ranges have spheroid boundaries. In this note, we characterize algebraic elementary operators in terms of Birkhoff-James orthogonality when they are induced by norm-attainable maps and the boundaries of their numerical ranges are spheroidal in shape. We show that under the spheroidicity criterion for the numerical range boundary, various types of algebraic elementary operators satisfy Birkhoff-James orthogonality.
Norm-attainment in locally convex spaces: Weak-* topology, inductive limits, and reflexivity
We characterize norm-attaining functionals in locally convex spaces (LCS), with particular focus on three fundamental aspects: the weak-* (weak-star) topology in dual spaces, inductive limits (including LF-spaces and DF-spaces), and reflexivity conditions. Our main results establish that (1) norm-attainment in the weak-* dual coincides precisely with the canonical embedding X into X**; (2) strict inductive limits (such as D(R)) permit non-attaining functionals, whereas Montel spaces ensure universal attainment; and (3) both barrelledness and reflexivity conditions recover norm-attainment through weak-* continuity. This work extends classical Banach space techniques to general LCS settings, revealing the crucial interplay between compactness properties and approximation methods in determining norm-attainment behavior.
Fixed point theorems of some mappings via interpolation in 2-Banach spaces
In this article, we introduce weak contractive mappings and interpolative Kannan-type contraction mappings on a 2-Banach space. In particular, we discuss the existence and uniqueness of a fixed point of such mappings in a 2-Banach space. However, we define interpolative Reich-Rus-Ćirić type contraction mappings and interpolative Hardy-Rogers type contraction mappings, Kannan-Ćirić type contraction mappings and interpolative Kannan-Meir-Keeler type contractions on a 2-Banach space. In particular, we prove the existence of a fixed point of such mappings in a 2-Banach space.
Some fixed point theorems in orbitally complete dq-metric space
This paper aims to obtain some new fixed point theorems in orbitally complete dislocated quasi-metric spaces for continuous self-mapping. This study opens new paths for research in dislocated quasi-metric spaces and enhances the ongoing progression of fixed point theory.
Orbitally complete dislocated quasi metric spaces
On Fuglede-Putnam property and orthogonality for derivations induced by hyponormal operators
The orthogonality of derivations induced by operators is an area with various applications in light of ever-dynamic technological advances. There are different types of orthogonality, and interesting results have emerged in which operators satisfying given conditions are chosen to establish Range-Kernel orthogonality. However, most of the results have focused on one type of orthogonality called the Birkhoff orthogonality. We have also herein considered the Birkhoff concept of orthogonality. Researchers have repeatedly posed the following question: Could there be a possibility for studying other types of orthogonality with respect to the range and the kernel of derivations apart from the Birkhoff orthogonality? In this note, we establish orthogonality conditions for derivations when implemented by hyponormal operators under the Fuglede-Putnam property.
On sufficient conditions for some classes of multivalent functions
In this paper, we investigate two distinct classes of multivalent functions and establish sufficient conditions for a multivalent function to belong to these classes. The results presented here extend and unify existing criteria related to the starlikeness and convexity of multivalently analytic functions. By generalizing earlier findings, our work provides a broader framework for analyzing geometric properties and inclusion relationships within subclasses of analytic multivalent functions.
Norm attainment and structural properties in Orlicz spaces: A comprehensive study on strict convexity, duality, and optimization
We investigate norm attainability and duality properties in Orlicz spaces, extending classical results from Banach and Hilbert spaces to a more gen- eral functional framework. We establish 14 fundamental theorems that character- ize norm attainment in terms of strict convexity, uniform convexity, and weak con- vergence. We explore the duality structure of Orlicz spaces, highlighting key differ- ences from Lp spaces and providing a variational characterization of the norm. We also discuss applications in optimization and variational problems, demonstrating the significance of norm-attaining functionals in these settings. Our findings con- tribute to a deeper understanding of Orlicz space geometry and its implications for functional analysis and applied mathematics.
Notes on fixed point results of C*-algebra-valued metric spaces
It is well-known that C* -algebras have been applied in understanding the physics of several phenomena in quantum theory, statistical mechanics and more than a handful of other domains. In continuation of these roles of C* - algebra, its notion has recently been incorporated in metric fixed point theory, and several results have been obtained thereof. However, in accordance with the existing literature, it is revealed that a collective and comparative analysis of the announced concepts of C* -algebra-valued metric spaces and the associated invariant point theorems has not been considered. One of the uses of such analysis is that it gives researchers handy information to know what has been done and the available gaps in the corresponding notions. With this background orientation, the objective of this paper is twofold: first, important developments of the idea of C* -algebra-valued metric spaces are surveyed. Thereafter, a comparative analysis of possible combinations and deductions based on the already obtained results is conducted. To achieve the latter objective, a few new results are formulated and non-trivial examples constructed, where necessary, to validate some of our observations.
Fixed point theorems for some mappings in 2-Banach spaces
In the present study, we introduce the notions of Meir-Keeler contrac- tion mappings and Ćirić contraction mappings on a 2-Banach space. In particular, we discuss the existence and uniqueness of a fixed point of such mappings in a 2-Banach space. On the other hand, we define the concept of Hardy-Rogers con- traction mappings on a 2-Banach space. In particular, we prove the existence and uniqueness of a fixed point of such a mapping in a 2-Banach space. However, many results are proved on fixed point theorems of some mappings in 2-Banach spaces.
The novel hybrid approach for solving time-fractional Fokker-Planck equations by the Tarig projected differential transform method
Fractional models offer greater accuracy and efficiency in modelling various physical systems across scientific, engineering, and technological fields. Analyzing linear and nonlinear time-fractional systems of fractional order differ- ential equations is a challenging task in terms of mathematical and theoretical aspects. In this paper, we propose a hybrid approach as a combination of the strength of the Tarig transform with the Projected Differential Transform Method (TPDTM) for solving the linear time-fractional Fokker-Planck (F-P) equation. The solution of the F-P equation was obtained in terms of space and fractional time co-ordinates based on imposing the different initial conditions. The results of the present work are illustrated using detailed 2D and 3D plots and tables for dif- ferent values of the fractional parameter, providing visual and numerical clarity on the behavior of the solutions. To validate the solution and evaluate the algorith- mic performance of the TPDTM, we have performed comparative analysis against solutions obtained using the Finite Difference Method (FDM), Homotopy Pertur- bation Method (HPM), and Laplace Adomian Decomposition Method (LADM) through different time fractional F-P equations. The study investigates solutions that show that TPDTM is a potent and straightforward technique for interpret- ing fractional F-P equations and is more versatile than FDM and HPM. Also, we found that our present work interpreted the high effectiveness and accuracy precision of results.
Projected differential trans- form method
Quadrature rule extended cubic spline approach for a class of nonlinear and linear Fredholm integral equations
In this research, we consider the linear and nonlinear Fredholm inte- gral equations (FIEs). The main aim of research is to approximate the integral by Gauss-Turán quadrature rule and then using an extended cubic spline as the base function. The unknown coefficients are determined in combination by the collocation method. The arising system of linear and nonlinear equations can be solved. Error analysis is investigated theoretically. Numerical text problems are considered to justify the applicability and efficient nature of our approach; com- parison of the results justifies the considerable accuracy and efficiency proposed methods. The extended parameter in valued in the spline can be chosen in such a way to improve the accuracy also.
A study of coincidence point theorems for multivalued mappings on extended m_b-metric spaces
In recent studies, the exploration of coincidence points represents a fresh development within the area of contractive-type single-valued and multival- ued theory. This paper establishes new coincidence point theorems pertaining to both single-valued and multivalued mappings within the context of extended mb-metric spaces. Employing methodologies derived from classical fixed point the- orems, such as Banach’s Contraction Principle and Kannan’s fixed point results, we elucidate the requisite conditions under which these mappings exhibit coinci- dence points. To underscore the practical implications of our principal theorem, we present an illustrative example that validates the results. These contributions advance the understanding of fixed point theory in extended mb-metric spaces and offer new avenues for further research in this area.
On fixed point results in S_b-metric spaces
In this paper, we present several fixed-point theorems for surjective mappings in complete S_b-metric spaces. We explore various conditions under which these fixed points exist.
Spectral theorems associated with the generalized Dunkl-Wigner localization operators
The main crux of this paper is to introduce the Wigner transform associated with the generalized Dunkl operator and to give some new results related to this transform. Next, we introduce a new class of pseudo-differential operator Lψ1,ψ2(σ) called localization operator which depends on a symbol σ and two admissible functions ψ1 and ψ2, we give a criteria in terms of the symbol σ for its boundedness and compactness, we also show that these operators belong to the Schatten-von Neumann class Sp for all p ∈ [1, +∞] and we give a trace formula.