Special Issue "New Trends in Analysis and Geometry"

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

Deadline for manuscript submissions: 31 July 2021.

Special Issue Editors

Prof. Dr. Mohamed Amine Khamsi
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Guest Editor
Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, USA
Interests: functional analysis; fixed point theory; operator theory; logic programming; ordered sets
Prof. Dr. Osvaldo Mendez
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Guest Editor
Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, USA
Interests: nonlinear functional analysis; PDE; harmonic analysis; variable exponent spaces; Musielak–Orlicz spaces; operator theory

Special Issue Information

Dear Colleagues,

The proposed Special Issue will encompass a wide variety of topics and will highlight the commonalities among areas that at first glance seem unrelated. Special emphasis will be placed on the interplay between fixed point theory and graph theory and the extension of some topics in analysis to the context of generalized metric spaces, in which the distance function takes values on a monoid...

 

 

Keywords

  • Fixed point theory
  • Variable exponent spaces
  • Weighted graphs
  • Generalized metric spaces
  • Non-expansive mappings
  • Modular spaces
  • Convex analysis
  • Nonlinear analysis
  • Regularity of PDE

Published Papers (5 papers)

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Research

Open AccessArticle
Ulam Type Stability of ?-Quadratic Mappings in Fuzzy Modular ∗-Algebras
Mathematics 2020, 8(9), 1630; https://doi.org/10.3390/math8091630 - 21 Sep 2020
Viewed by 372
Abstract
In this paper, we find the solution of the following quadratic functional equation n1i<jnQxixj=i=1nQjixj( [...] Read more.
In this paper, we find the solution of the following quadratic functional equation n1i<jnQxixj=i=1nQjixj(n1)xi, which is derived from the gravity of the n distinct vectors x1,,xn in an inner product space, and prove that the stability results of the A-quadratic mappings in μ-complete convex fuzzy modular ∗-algebras without using lower semicontinuity and β-homogeneous property. Full article
(This article belongs to the Special Issue New Trends in Analysis and Geometry)
Open AccessFeature PaperArticle
Modular Uniform Convexity in Every Direction in Lp(·) and Its Applications
Mathematics 2020, 8(6), 870; https://doi.org/10.3390/math8060870 - 28 May 2020
Viewed by 421
Abstract
We prove that the Lebesgue space of variable exponent L p ( · ) ( Ω ) is modularly uniformly convex in every direction provided the exponent p is finite a.e. and different from 1 a.e. The notion of uniform convexity in every [...] Read more.
We prove that the Lebesgue space of variable exponent L p ( · ) ( Ω ) is modularly uniformly convex in every direction provided the exponent p is finite a.e. and different from 1 a.e. The notion of uniform convexity in every direction was first introduced by Garkavi for the case of a norm. The contribution made in this work lies in the discovery of a modular, uniform-convexity-like structure of L p ( · ) ( Ω ) , which holds even when the behavior of the exponent p ( · ) precludes uniform convexity of the Luxembourg norm. Specifically, we show that the modular ρ ( u ) = Ω | u ( x ) | d x possesses a uniform-convexity-like structure even if the variable exponent is not bounded away from 1 or . Our result is new and we present an application to fixed point theory. Full article
(This article belongs to the Special Issue New Trends in Analysis and Geometry)
Open AccessArticle
Existence of Solutions for a System of Integral Equations Using a Generalization of Darbo’s Fixed Point Theorem
Mathematics 2020, 8(4), 492; https://doi.org/10.3390/math8040492 - 01 Apr 2020
Viewed by 415
Abstract
In this paper, an extension of Darbo’s fixed point theorem via θ -F-contractions in a Banach space has been presented. Measure of noncompactness approach is the main tool in the presentation of our proofs. As an application, we study the existence [...] Read more.
In this paper, an extension of Darbo’s fixed point theorem via θ -F-contractions in a Banach space has been presented. Measure of noncompactness approach is the main tool in the presentation of our proofs. As an application, we study the existence of solutions for a system of integral equations. Finally, we present a concrete example to support the effectiveness of our results. Full article
(This article belongs to the Special Issue New Trends in Analysis and Geometry)
Open AccessArticle
Conjugacy of Dynamical Systems on Self-Similar Groups
Mathematics 2020, 8(2), 226; https://doi.org/10.3390/math8020226 - 10 Feb 2020
Viewed by 362
Abstract
We show that the limits for dynamical systems of self-similar groups are eventually conjugate if, and only if, there is an isomorphism between their Deaconu groupoid preserving cocycles. For limit solenoids of self-similar groups, we show that the conjugacy of limit solenoids is [...] Read more.
We show that the limits for dynamical systems of self-similar groups are eventually conjugate if, and only if, there is an isomorphism between their Deaconu groupoid preserving cocycles. For limit solenoids of self-similar groups, we show that the conjugacy of limit solenoids is equivalent to existence of isomorphism between the Deaconu groupoids of limit solenoid preserving cocycles. Full article
(This article belongs to the Special Issue New Trends in Analysis and Geometry)
Open AccessArticle
Fixed Points of Kannan Maps in the Variable Exponent Sequence Spaces p(·)
Mathematics 2020, 8(1), 76; https://doi.org/10.3390/math8010076 - 03 Jan 2020
Cited by 1 | Viewed by 724
Abstract
Kannan maps have inspired a branch of metric fixed point theory devoted to the extension of the classical Banach contraction principle. The study of these maps in modular vector spaces was attempted timidly and was not successful. In this work, we look at [...] Read more.
Kannan maps have inspired a branch of metric fixed point theory devoted to the extension of the classical Banach contraction principle. The study of these maps in modular vector spaces was attempted timidly and was not successful. In this work, we look at this problem in the variable exponent sequence spaces p ( · ) . We prove the modular version of most of the known facts about these maps in metric and Banach spaces. In particular, our results for Kannan nonexpansive maps in the modular sense were never attempted before. Full article
(This article belongs to the Special Issue New Trends in Analysis and Geometry)
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