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

Deadline for manuscript submissions: closed (31 July 2023) | Viewed by 13144

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Special Issue Editors

Dr. Muhammed Mursaleen

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Guest Editor

Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Interests: functional analysis; operator theory; approximation theory; fixed point theory; applications to differential and integral equations

Dr. Mikail Et

E-Mail Website
Guest Editor

Department of Mathematics, Fırat University, 23119 Elazığ, Turkey
Interests: sequence spaces; fuzzy sequence; dual spaces; statistical convergence; geometrics properties

Special Issue Information

Dear Colleagues,

The aim of this Special Issue is to focus on the advances in Banach spaces, matrix transformations, symmetry, and their various developments and applications in operators, differential and integral equations, functional equations, symmetry, and other related areas. The framework of Banach spaces has been considered by many researchers to obtain the existence of solutions of differential and integral equations. We stress that symmetry plays an important role in proving the Banach–Steinhaus uniform boundedness principle, while this theorem is considered one of the cornerstones of the theory of functional analysis associated with normed space (and therefore Banach space as well). The theory of matrices or matrix transformations has significance in a variety of problems, including Fourier analysis, approximation of operators, symmetry, and analytic continuation, to name a few.

We cordially invite researchers to submit novel research and review articles that will contribute to the ongoing study of the theory of Banach spaces, matrix transformations, and symmetry. Potential topics include but are not limited to the following:

The geometry, topology and symmetry of Banach spaces;
Solvability of differential and integral equations in Banach spaces;
Matrix transformations, associated compact operators and symmetry;
Approximation of positive operators and symmetry;
Fixed-point theory and applications;
Summability methods associated with symmetry.

Submit your paper and select the Journal “Symmetry” and the Special Issue “Advances in Matrix Transformations, Operators and Symmetry” via: MDPI submission system. Our papers will be published on a rolling basis and we will be pleased to receive your submission once you have finished it.

Dr. Muhammed Mursaleen
Dr. Mikail Et
Guest Editors

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.

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Published Papers (7 papers)

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Research

12 pages, 283 KiB

Open AccessArticle

Modulated Lacunary Statistical and Strong-Cesàro Convergences

by María del Pilar Romero de la Rosa

Symmetry 2023, 15(7), 1351; https://doi.org/10.3390/sym15071351 - 3 Jul 2023

Viewed by 792

Abstract

Here, we continued the studies initiated by Vinod K. Bhardwaj and Shweta Dhawan which relate different convergence methods involving the classical statistical and the classical strong Cesàro convergences by means of lacunary sequences and measures of density in

N

modulated by a modulus [...] Read more.

N

modulated by a modulus function f. A method for constructing non-compatible modulus functions was also included, which is related to symmetries with respect to

y = x

. Full article

(This article belongs to the Special Issue Advances in Matrix Transformations, Operators and Symmetry)

32 pages, 548 KiB

Open AccessArticle

Terracini Loci of Segre Varieties

by Edoardo Ballico

Symmetry 2022, 14(11), 2440; https://doi.org/10.3390/sym14112440 - 17 Nov 2022

Cited by 1 | Viewed by 1176

Abstract

Fix a format

(n_{1} + 1) \times \dots \times (n_{k} + 1)

k > 1

, for real or complex tensors and the associated multiprojective space Y. Let V be the vector space of all [...] Read more.

Fix a format

(n_{1} + 1) \times \dots \times (n_{k} + 1)

k > 1

, for real or complex tensors and the associated multiprojective space Y. Let V be the vector space of all tensors of the prescribed format. Let

S (Y, x)

denote the set of all subsets of Y with cardinality x. Elements of

S (Y, x)

are associated to rank 1 decompositions of tensors

T \in V

. We study the dimension

δ (2 S, Y)

of the kernel at S of the differential of the associated algebraic map

S (Y, x) \overset{}{\to} P V

. The set

T_{1} (Y, x)

of all

S \in S (Y, x)

such that

δ (2 S, Y) > 0

is the largest and less interesting x-Terracini locus for tensors

T \in V

. Moreover, we consider the one (minimally Terracini) such that

δ (2 A, Y) = 0

for all

A ⊈ S

. We define and study two different types of subsets of

T_{1} (Y, x)

(primitive Terracini and solution sets). A previous work (Ballico, Bernardi, and Santarsiero) provided a complete classification for the cases

x = 2, 3

. We consider the case

x = 4

and several extremal cases for arbitrary x. Full article

(This article belongs to the Special Issue Advances in Matrix Transformations, Operators and Symmetry)

8 pages, 263 KiB

Open AccessArticle

Statistical Convergence of Δ-Spaces Using Fractional Order

by Mashael M. AlBaidani

Symmetry 2022, 14(8), 1685; https://doi.org/10.3390/sym14081685 - 14 Aug 2022

Viewed by 1559

Abstract

The notion of fractional structures has been studied intensely in various fields. Using this concept, the main idea of this paper is to apply the Cesàro approach and introduce the new generalized

Δ

-structure of spaces on a fractional level. Also, the statistical [...] Read more.

The notion of fractional structures has been studied intensely in various fields. Using this concept, the main idea of this paper is to apply the Cesàro approach and introduce the new generalized

Δ

-structure of spaces on a fractional level. Also, the statistical notions will be studied using this new structure and some inclusion relations will be computed. In addition, the sequence space

W_{q} (Δ_{g}^{κ}, f)

will be introduced, and some fundamental inclusion relations and topological properties concerning it will be given. Full article

(This article belongs to the Special Issue Advances in Matrix Transformations, Operators and Symmetry)

19 pages, 360 KiB

Open AccessArticle

A Generalization of Szász–Mirakyan Operators Based on α Non-Negative Parameter

by Khursheed J. Ansari and Fuat Usta

Symmetry 2022, 14(8), 1596; https://doi.org/10.3390/sym14081596 - 3 Aug 2022

Cited by 5 | Viewed by 1506

Abstract

The main purpose of this paper is to define a new family of Szász–Mirakyan operators that depends on a non-negative parameter, say

α

. This new family of Szász–Mirakyan operators is crucial in that it includes both the existing Szász–Mirakyan operator and allows [...] Read more.

The main purpose of this paper is to define a new family of Szász–Mirakyan operators that depends on a non-negative parameter, say

α

. This new family of Szász–Mirakyan operators is crucial in that it includes both the existing Szász–Mirakyan operator and allows the construction of new operators for different values of

α

. Then, the convergence properties of the new operators with the aid of the Popoviciu–Bohman–Korovkin theorem-type property are presented. The Voronovskaja-type theorem and rate of convergence are provided in a detailed proof. Furthermore, with the help of the classical modulus of continuity, we deduce an upper bound for the error of the new operator. In addition to these, in order to show that the convex or monotonic functions produced convex or monotonic operators, we obtain shape-preserving properties of the new family of Szász–Mirakyan operators. The symmetry of the properties of the classical Szász–Mirakyan operator and of the properties of the new sequence is investigated. Moreover, we compare this operator with its classical correspondence to show that the new one has superior properties. Finally, some numerical illustrative examples are presented to strengthen our theoretical results. Full article

(This article belongs to the Special Issue Advances in Matrix Transformations, Operators and Symmetry)

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17 pages, 381 KiB

Open AccessArticle

New Parallel Fixed Point Algorithms and Their Application to a System of Variational Inequalities

by Samet Maldar

Symmetry 2022, 14(5), 1025; https://doi.org/10.3390/sym14051025 - 17 May 2022

Cited by 1 | Viewed by 1576

Abstract

In this study, considering the advantages of parallel fixed point algorithms arising from their symmetrical behavior, new types of parallel algorithms have been defined. Strong convergence of these algorithms for certain mappings with altering points has been analyzed, and it has been observed that their convergence behavior is better than existing algorithms with non-simple samples. In addition, the concept of data dependency for these algorithms has been examined for the first time in this study. Finally, it has been proven that the solution of a variational inequality system can be obtained using newly defined parallel algorithms under suitable conditions. Full article

(This article belongs to the Special Issue Advances in Matrix Transformations, Operators and Symmetry)

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14 pages, 342 KiB

Open AccessArticle

The Spectrum of Second Order Quantum Difference Operator

by Taja Yaying, Bipan Hazarika, Binod Chandra Tripathy and Mohammad Mursaleen

Symmetry 2022, 14(3), 557; https://doi.org/10.3390/sym14030557 - 10 Mar 2022

Cited by 12 | Viewed by 2192

Abstract

In this study, we give another generalization of second order backward difference operator

\nabla^{2}

by introducing its quantum analog

\nabla_{q}^{2} .

The operator

\nabla_{q}^{2}

represents the third band infinite matrix. We construct its domains [...] Read more.

In this study, we give another generalization of second order backward difference operator

\nabla^{2}

by introducing its quantum analog

\nabla_{q}^{2} .

The operator

\nabla_{q}^{2}

represents the third band infinite matrix. We construct its domains

c_{0} (\nabla_{q}^{2})

and

c (\nabla_{q}^{2})

in the spaces

c_{0}

and c of null and convergent sequences, respectively, and establish that the domains

c_{0} (\nabla_{q}^{2})

and

c (\nabla_{q}^{2})

are Banach spaces linearly isomorphic to

c_{0}

and

c,

respectively, and obtain their Schauder bases and

α

β

- and

γ

-duals. We devote the last section to determine the spectrum, the point spectrum, the continuous spectrum and the residual spectrum of the operator

\nabla_{q}^{2}

over the Banach space

c_{0}

of null sequences. Full article

(This article belongs to the Special Issue Advances in Matrix Transformations, Operators and Symmetry)

12 pages, 285 KiB

Open AccessArticle

Two Dimensional Laplace Transform Coupled with the Marichev-Saigo-Maeda Integral Operator and the Generalized Incomplete Hypergeometric Function

by Yasir Khan, Adnan Khan, Muhammad Shaeel and Ali Akgül

Symmetry 2021, 13(12), 2420; https://doi.org/10.3390/sym13122420 - 14 Dec 2021

Cited by 4 | Viewed by 2227

Abstract

This paper represents the processing of the two-dimensional Laplace transform with the two-dimensional Marichev–Saigo–Maeda integral operators and two-dimensional incomplete hypergeometric function. This article provides an entirely new perspective on the Marichev–Saigo–Maeda operators and incomplete functions. In addition, we have included some interesting results, [...] Read more.

(This article belongs to the Special Issue Advances in Matrix Transformations, Operators and Symmetry)

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