Iterative Numerical Functional Analysis with Applications, Volume 3

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 30 June 2024 | Viewed by 2406

Special Issue Editor

Special Issue Information

Dear Colleagues,

A plethora of problems from diverse disciplines such as applied mathematics, dynamics of physical systems, mathematical biology, chemistry, economics, physics, statistics, and also engineering, to mention a few, can be written in solving an equation or systems of equations in abstract spaces such as the Euclidean space, Hilbert, Banach or other spaces. The solution is preferred in closed form, but this is possible only in special cases.

That is why researchers and practitioners are resorting to developing iterative methods generating a sequence converging to the solution under certain conditions on the initial data. Therefore, we invite papers in this and related areas. Papers solving ordinary or partial differential or integral equations in abstract spaces are especially invited.

Specially selected review papers connecting this with other areas are also welcome.

Prof. Dr. Ioannis K. Argyros
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (2 papers)

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Research

15 pages, 2709 KiB  
Article
A New Iterative Method for Investigating Modified Camassa–Holm and Modified Degasperis–Procesi Equations within Caputo Operator
by Humaira Yasmin, Yousuf Alkhezi and Khaled Alhamad
Symmetry 2023, 15(12), 2172; https://doi.org/10.3390/sym15122172 - 7 Dec 2023
Cited by 2 | Viewed by 973
Abstract
In this paper, we employ the new iterative method to investigate two prominent nonlinear partial differential equations, namely the modified Camassa–Holm (mCH) equation and the modified Degasperis–Procesi (mDP) equation, both within the framework of the Caputo operator. The mCH and mDP equations are [...] Read more.
In this paper, we employ the new iterative method to investigate two prominent nonlinear partial differential equations, namely the modified Camassa–Holm (mCH) equation and the modified Degasperis–Procesi (mDP) equation, both within the framework of the Caputo operator. The mCH and mDP equations are fundamental in studying wave propagation and soliton dynamics, exhibiting complex behavior and intriguing mathematical structures. The new iterative method (NIM), a powerful numerical technique, is utilized to obtain analytical and numerical solutions for these equations, offering insights into their dynamic properties and behavior. Through systematic analysis and computation, we unveil the unique features of the mCH and the mDP equations, shedding light on their applicability in various scientific and engineering domains. This research contributes to the ongoing exploration of nonlinear wave equations and their solutions, emphasizing the versatility of the new iterative method in tackling complex mathematical problems. Numerical results and comparative analyses are presented to validate the effectiveness of the new iterative method in solving these equations, highlighting its potential for broader applications in mathematical modeling and analysis. Full article
(This article belongs to the Special Issue Iterative Numerical Functional Analysis with Applications, Volume 3)
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22 pages, 350 KiB  
Article
Generalized Common Best Proximity Point Results in Fuzzy Metric Spaces with Application
by Umar Ishtiaq, Fahad Jahangeer, Doha A. Kattan and Ioannis K. Argyros
Symmetry 2023, 15(8), 1501; https://doi.org/10.3390/sym15081501 - 28 Jul 2023
Cited by 1 | Viewed by 1066
Abstract
The symmetry of fuzzy metric spaces has benefits for flexibility, ambiguity tolerance, resilience, compatibility, and applicability. They provide a more comprehensive description of similarity and offer a solid framework for working with ambiguous and imprecise data. We give fuzzy versions of some celebrated [...] Read more.
The symmetry of fuzzy metric spaces has benefits for flexibility, ambiguity tolerance, resilience, compatibility, and applicability. They provide a more comprehensive description of similarity and offer a solid framework for working with ambiguous and imprecise data. We give fuzzy versions of some celebrated iterative mappings. Further, we provide different concrete conditions on the real valued functions J,S:(0,1]R for the existence of the best proximity point of generalized fuzzy (J,S)-iterative mappings in the setting of fuzzy metric space. Furthermore, we utilize fuzzy versions of J,S-proximal contraction, J,S-interpolative Reich–Rus–Ciric-type proximal contractions, J,S-Kannan type proximal contraction and J,S-interpolative Hardy Roger’s type proximal contraction to examine the common best proximity points in fuzzy metric space. Also, we establish several non-trivial examples and an application to support our results. Full article
(This article belongs to the Special Issue Iterative Numerical Functional Analysis with Applications, Volume 3)
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