Mathematics

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22 pages, 342 KiB

Open AccessArticle

Applications to Boundary Value Problems and Homotopy Theory via Tripled Fixed Point Techniques in Partially Metric Spaces

by Hasanen A. Hammad, Praveen Agarwal and Juan L. G. Guirao

Mathematics 2021, 9(16), 2012; https://doi.org/10.3390/math9162012 - 23 Aug 2021

Cited by 24 | Viewed by 1713

Abstract

In this manuscript, some tripled fixed point results were derived under

(φ, ρ, ℓ)

-contraction in the framework of ordered partially metric spaces. Moreover, we furnish an example which supports our theorem. Furthermore, some results about a homotopy results [...] Read more.

In this manuscript, some tripled fixed point results were derived under

(φ, ρ, ℓ)

-contraction in the framework of ordered partially metric spaces. Moreover, we furnish an example which supports our theorem. Furthermore, some results about a homotopy results are obtained. Finally, theoretical results are involved in some applications, such as finding the unique solution to the boundary value problems and homotopy theory. Full article

(This article belongs to the Special Issue New Trends in Analysis and Geometry)

13 pages, 274 KiB

Open AccessArticle

Ulam Type Stability of ?-Quadratic Mappings in Fuzzy Modular ∗-Algebras

by Hark-Mahn Kim and Hwan-Yong Shin

Mathematics 2020, 8(9), 1630; https://doi.org/10.3390/math8091630 - 21 Sep 2020

Viewed by 1544

Abstract

In this paper, we find the solution of the following quadratic functional equation [...] Read more.

In this paper, we find the solution of the following quadratic functional equation

n \sum_{1 \leq i < j \leq n} Q (x_{i} - x_{j}) = \sum_{i = 1}^{n} Q (\sum_{j \neq i} x_{j} - (n - 1) x_{i})

, which is derived from the gravity of the n distinct vectors

x_{1}, \dots, x_{n}

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)

12 pages, 311 KiB

Open AccessFeature PaperArticle

Modular Uniform Convexity in Every Direction in L^p(·) and Its Applications

by Mostafa Bachar and Osvaldo Méndez

Mathematics 2020, 8(6), 870; https://doi.org/10.3390/math8060870 - 28 May 2020

Cited by 2 | Viewed by 1599

Abstract

We prove that the Lebesgue space of variable exponent

L^{p (\cdot)} (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 (\cdot)} (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 (\cdot)} (Ω)

, which holds even when the behavior of the exponent

p (\cdot)

precludes uniform convexity of the Luxembourg norm. Specifically, we show that the modular

ρ (u) = \int_{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)

11 pages, 277 KiB

Open AccessArticle

Existence of Solutions for a System of Integral Equations Using a Generalization of Darbo’s Fixed Point Theorem

by Babak Mohammadi, Ali Asghar Shole Haghighi, Maryam Khorshidi, Manuel De la Sen and Vahid Parvaneh

Mathematics 2020, 8(4), 492; https://doi.org/10.3390/math8040492 - 1 Apr 2020

Cited by 13 | Viewed by 2043

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)

12 pages, 262 KiB

Open AccessArticle

Conjugacy of Dynamical Systems on Self-Similar Groups

by Inhyeop Yi

Mathematics 2020, 8(2), 226; https://doi.org/10.3390/math8020226 - 10 Feb 2020

Cited by 1 | Viewed by 1353

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)

7 pages, 277 KiB

Open AccessArticle

Fixed Points of Kannan Maps in the Variable Exponent Sequence Spaces ℓ_p(·)

by Afrah A. N. Abdou and Mohamed Amine Khamsi

Mathematics 2020, 8(1), 76; https://doi.org/10.3390/math8010076 - 3 Jan 2020

Cited by 4 | Viewed by 2145

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

ℓ_{p (\cdot)}

. 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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