Mathematical Analysis and Functional Analysis and Their Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: 30 June 2024 | Viewed by 6765

Special Issue Editor

School of Mathematical and Statistical Science, The University of Texas Rio Grande Valley, Edinberg, TX 78540, USA
Interests: mathematical physics; differential geometry; functional analysis
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Special Issue Information

Dear Colleagues,

The intention of this special issue on Functional Analysis is intended to cover all aspects of current research work on the subject. Papers are invited from those who work in functional analysis proper or in any one of the areas in which functional analysis is usually applied. This may incluse operators in Hilbert spaces, self-adjoint operators, Sobolev spaces, weak derivatives, elliptic problems, distributions, semigroups of linear operators, weakly nonlinear equations and nonlinear equations, and parabolic equations. There has also been a great deal of interest in applications to the area of dynamical systems and related areas. Moreover, if an author has a particular idea in mind, it may also be considered as a topic as long as it is related to the main subject of this issue.

Prof. Dr. Paul Bracken
Guest Editor

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Keywords

  • functional analysis and operators
  • sobolov spaces
  • weakly nonlinear equations
  • applications to dynamical systems theory
  • application in differential geometry

Published Papers (6 papers)

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Research

14 pages, 312 KiB  
Article
Inverse Problem for a Fourth-Order Hyperbolic Equation with a Complex-Valued Coefficient
Mathematics 2023, 11(15), 3432; https://doi.org/10.3390/math11153432 - 07 Aug 2023
Cited by 2 | Viewed by 562
Abstract
This paper studies the existence and uniqueness of the classical solution of inverse problems for a fourth-order hyperbolic equation with a complex-valued coefficient with Dirichlet and Neumann boundary conditions. Using the method of separation of variables, formal solutions are obtained in the form [...] Read more.
This paper studies the existence and uniqueness of the classical solution of inverse problems for a fourth-order hyperbolic equation with a complex-valued coefficient with Dirichlet and Neumann boundary conditions. Using the method of separation of variables, formal solutions are obtained in the form of a Fourier series in terms of the eigenfunctions of a non-self-adjoint fourth-order ordinary differential operator. The proofs of the uniform convergence of the Fourier series are based on estimates of the norms of the derivatives of the eigenfunctions of a fourth-order ordinary differential operator and the uniform boundedness of the Riesz bases of the eigenfunctions. Full article
(This article belongs to the Special Issue Mathematical Analysis and Functional Analysis and Their Applications)
15 pages, 315 KiB  
Article
Characterization Results on Lifetime Distributions by Scaled Reliability Measures Using Completeness Property in Functional Analysis
Mathematics 2023, 11(6), 1547; https://doi.org/10.3390/math11061547 - 22 Mar 2023
Viewed by 768
Abstract
In this article, using the scaled (weighted) residual life variable, some scaled measures, the scaled mean residual life and the scaled hazard rate, are introduced. Several scales are considered as examples of the derivation of the scaled measures. The measures are developed for [...] Read more.
In this article, using the scaled (weighted) residual life variable, some scaled measures, the scaled mean residual life and the scaled hazard rate, are introduced. Several scales are considered as examples of the derivation of the scaled measures. The measures are developed for the case of a weighted residual life at a random time, and it is shown that the measures are scale-free in these cases. This property proves useful in situations where a relative comparison of the lifetime distribution is studied. Some characterization properties are derived in terms of scaled measures evaluated at some sequences of random time points that follow a typical distribution. Examples are used to illustrate, examine, and satisfy the obtained characterizations. Full article
(This article belongs to the Special Issue Mathematical Analysis and Functional Analysis and Their Applications)
26 pages, 465 KiB  
Article
A New Four-Step Iterative Procedure for Approximating Fixed Points with Application to 2D Volterra Integral Equations
Mathematics 2022, 10(22), 4257; https://doi.org/10.3390/math10224257 - 14 Nov 2022
Cited by 5 | Viewed by 1013
Abstract
This work is devoted to presenting a new four-step iterative scheme for approximating fixed points under almost contraction mappings and Reich–Suzuki-type nonexpansive mappings (RSTN mappings, for short). Additionally, we demonstrate that for almost contraction mappings, the proposed algorithm converges faster than a variety [...] Read more.
This work is devoted to presenting a new four-step iterative scheme for approximating fixed points under almost contraction mappings and Reich–Suzuki-type nonexpansive mappings (RSTN mappings, for short). Additionally, we demonstrate that for almost contraction mappings, the proposed algorithm converges faster than a variety of other current iterative schemes. Furthermore, the new iterative scheme’s ω2—stability result is established and a corroborating example is given to clarify the concept of ω2—stability. Moreover, weak as well as a number of strong convergence results are demonstrated for our new iterative approach for fixed points of RSTN mappings. Further, to demonstrate the effectiveness of our new iterative strategy, we also conduct a numerical experiment. Our major finding is applied to demonstrate that the two-dimensional (2D) Volterra integral equation has a solution. Additionally, a comprehensive example for validating the outcome of our application is provided. Our results expand and generalize a number of relevant results in the literature. Full article
(This article belongs to the Special Issue Mathematical Analysis and Functional Analysis and Their Applications)
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18 pages, 307 KiB  
Article
New Generalized Contractions by Employing Two Control Functions and Coupled Fixed-Point Theorems with Applications
Mathematics 2022, 10(17), 3208; https://doi.org/10.3390/math10173208 - 05 Sep 2022
Viewed by 763
Abstract
In this study, we obtain certain coupled fixed-point results for generalized contractions involving two control functions in a controlled metric space. Additionally, we establish some coupled fixed-point results in graph-enabled controlled metric spaces. Many well-known results from the literature will be expanded upon [...] Read more.
In this study, we obtain certain coupled fixed-point results for generalized contractions involving two control functions in a controlled metric space. Additionally, we establish some coupled fixed-point results in graph-enabled controlled metric spaces. Many well-known results from the literature will be expanded upon and modified by our results. In order to demonstrate the validity of the stated results, we also offer some examples. Finally, we apply the theoretical results to obtain the solution to a system of integral equations. Full article
(This article belongs to the Special Issue Mathematical Analysis and Functional Analysis and Their Applications)
10 pages, 264 KiB  
Article
The Results on Coincidence and Common Fixed Points for a New Type Multivalued Mappings in b-Metric Spaces
Mathematics 2022, 10(6), 856; https://doi.org/10.3390/math10060856 - 08 Mar 2022
Cited by 3 | Viewed by 1436
Abstract
In this paper, we obtain the results of coincidence and common fixed points in b-metric spaces. We work with a new type of multivalued quasi-contractive mapping with nonlinear comparison functions. Our results generalize and improve several recent results. Additionally, we give an [...] Read more.
In this paper, we obtain the results of coincidence and common fixed points in b-metric spaces. We work with a new type of multivalued quasi-contractive mapping with nonlinear comparison functions. Our results generalize and improve several recent results. Additionally, we give an application of the obtained results to dynamical systems. Full article
(This article belongs to the Special Issue Mathematical Analysis and Functional Analysis and Their Applications)
13 pages, 364 KiB  
Article
Liouville-Type Results for a Three-Dimensional Eyring-Powell Fluid with Globally Bounded Spatial Gradients in Initial Data
Mathematics 2022, 10(5), 741; https://doi.org/10.3390/math10050741 - 26 Feb 2022
Cited by 2 | Viewed by 993
Abstract
The analysis in the present paper provides insights into the Liouville-type results for an Eyring-Powell fluid considered as having an incompressible and unsteady flow. The gradients in the spatial distributions of the initial data are assumed to be globally (in the sense of [...] Read more.
The analysis in the present paper provides insights into the Liouville-type results for an Eyring-Powell fluid considered as having an incompressible and unsteady flow. The gradients in the spatial distributions of the initial data are assumed to be globally (in the sense of energy) bounded. Under this condition, solutions to the Eyring-Powell fluid equations are regular and bounded under the L2 norm. Additionally, a numerical assessment is provided to show the mentioned regularity of solutions in the travelling wave domain. This exercise serves as a validation of the analytical approach firstly introduced. Full article
(This article belongs to the Special Issue Mathematical Analysis and Functional Analysis and Their Applications)
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