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26 pages, 6013 KB

Open AccessArticle

Dynamic Responseof Complex Defect near Anisotropic Bi-Material Interface by Incident Out-Plane Wave

by Huanan Xu, Caizhu Yang, Yonghui Wang, Guoguan Lan and Faqiang Qiu

Symmetry 2025, 17(5), 778; https://doi.org/10.3390/sym17050778 - 17 May 2025

Viewed by 891

The Dynamic response of two cavities, an elliptical inclusion and a linear crack near anisotropic bi-material interface, was explored analytically by incident out-plane waves in the current work. Firstly, the media is divided into two half spaces (an elastic anisotropic half space with a circular cavity and a linear crack, and an elastic isotropic half space containing an elliptical cavity and an elliptical inclusion). With the help of the image principle, the complex function method is then used to derive the wave fields in each half space. Combined with Green’s functions approach, the relevant Green’s functions developed in the “crack creation” and “conjunction of two half spaces” procedures are derived sequentially. Subsequently, based on the “conjunction” technique, undetermined anti-plane forces are applied to the horizontal surfaces of two half spaces to maintain the continuity criteria of the interface. A series of Fredholm integral equations isobtained and then solved by utilizing the direct discrete technique. Dynamic stress concentration of two elliptical cavities and an elliptical inclusion is mainly considered graphically to discuss the interaction between two half spaces. Finally, a parametric study on the dynamic stress concentration factor (DSCF) was given to show the influence of different parameters on the interaction. Full article

(This article belongs to the Section Mathematics)

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19 pages, 835 KB

Open AccessArticle

Convergence Analysis for Generalized Yosida Inclusion Problem with Applications

by Mohammad Akram, Mohammad Dilshad, Aysha Khan, Sumit Chandok and Izhar Ahmad

Mathematics 2023, 11(6), 1409; https://doi.org/10.3390/math11061409 - 14 Mar 2023

Cited by 2 | Viewed by 1822

Abstract

A new generalized Yosida inclusion problem, involving

A

A new generalized Yosida inclusion problem, involving

A

-relaxed co-accretive mapping, is introduced. The resolvent and associated generalized Yosida approximation operator is construed and a few of its characteristics are discussed. The existence result is quantified in q-uniformly smooth Banach spaces. A four-step iterative scheme is proposed and its convergence analysis is discussed. Our theoretical assertions are illustrated by a numerical example. In addition, we confirm that the developed method is almost stable for contractions. Further, an equivalent generalized resolvent equation problem is established. Finally, by utilizing the Yosida inclusion problem, we investigate a resolvent equation problem and by employing our proposed method, a Volterra–Fredholm integral equation is examined. Full article

23 pages, 404 KB

Open AccessArticle

Hybrid Fuzzy Contraction Theorems with Their Role in Integral Inclusions

by Faryad Ali, Mohammed Shehu Shagari and Akbar Azam

Axioms 2022, 11(11), 580; https://doi.org/10.3390/axioms11110580 - 22 Oct 2022

Viewed by 1761

Abstract

The focus of this paper is to establish a new concept of b-hybrid fuzzy contraction regarding the study of fuzzy fixed-point theorems in the setting of b-metric spaces. This idea harmonizes and refines several well-known results in the direction of point-valued, multivalued, and fuzzy-set-valued maps in the comparable literature. To attract new researchers to this field, some important results are shown to be corollaries. Moreover, a result is presented to establish sufficient conditions for the existence of solutions of integral inclusion of Fredholm type. Lastly, illustrations are presented to validate the suppositions of the given theorems. Full article

(This article belongs to the Special Issue Fixed Point Theory and Its Related Topics III)

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11 pages, 265 KB

Open AccessArticle

Some New Fixed Point Theorems in b-Metric Spaces with Application

by Badriah A. S. Alamri, Ravi P. Agarwal and Jamshaid Ahmad

Mathematics 2020, 8(5), 725; https://doi.org/10.3390/math8050725 - 4 May 2020

Cited by 7 | Viewed by 2557

Abstract

The aim of this article is to introduce a new class of contraction-like mappings, called the almost multivalued (

Θ, δ_{b}

)-contraction mappings in the setting of b-metric spaces to obtain some generalized fixed point theorems. As an application of [...] Read more.

The aim of this article is to introduce a new class of contraction-like mappings, called the almost multivalued (

Θ, δ_{b}

)-contraction mappings in the setting of b-metric spaces to obtain some generalized fixed point theorems. As an application of our main result, we present the sufficient conditions for the existence of solutions of Fredholm integral inclusions. An example is also provided to verify the effectiveness and applicability of our main results. Full article

19 pages, 288 KB

Open AccessArticle

Solutions to Fredholm Integral Inclusions via Generalized Fuzzy Contractions

by Hamed H Al-Sulami, Jamshaid Ahmad, Nawab Hussain and Abdul Latif

Mathematics 2019, 7(9), 808; https://doi.org/10.3390/math7090808 - 2 Sep 2019

Cited by 5 | Viewed by 2087

Abstract

The aim of this study is to investigate the existence of solutions for the following Fredholm integral inclusion [...] Read more.

The aim of this study is to investigate the existence of solutions for the following Fredholm integral inclusion

φ (t) \in [f (t) + \int_{0}^{1} K (t, s, φ (s)) ϱ s]

for

t \in [0, 1],

where

f \in C [0, 1]

is a given real-valued function and

K : [0, 1]

\times [0, 1]

\times R \to K_{c v} (R)

a given multivalued operator, where

K_{c v}

represents the family of non-empty compact and convex subsets of

R

φ \in C [0, 1]

is the unknown function and

ϱ

is a metric defined on

C [0, 1]

. To attain this target, we take advantage of fixed point theorems for

α

-fuzzy mappings satisfying a new class of contractive conditions in the context of complete metric spaces. We derive new fixed point results which extend and improve the well-known results of Banach, Kannan, Chatterjea, Reich, Hardy-Rogers, Berinde and Ćirić by means of this new class of contractions. We also give a significantly non-trivial example to support our new results. Full article

12 pages, 263 KB

Open AccessArticle

Generalized Fixed-Point Results for Almost (α,F_σ)-Contractions with Applications to Fredholm Integral Inclusions

by Saleh Abdullah Al-Mezel and Jamshaid Ahmad

Symmetry 2019, 11(9), 1068; https://doi.org/10.3390/sym11091068 - 21 Aug 2019

Cited by 7 | Viewed by 2822

Abstract

The purpose of this article is to define almost

(α, F_{σ})

-contractions and establish some generalized fixed-point results for a new class of contractive conditions in the setting of complete metric spaces. In application, we apply our fixed-point theorem [...] Read more.

The purpose of this article is to define almost

(α, F_{σ})

ϖ (t) \in [f (t) + \int_{0}^{1} K (t, s, x (s)) ϑ s], t \in [0, 1]

where

f \in C [0, 1]

is a given real-valued function and

K : [0, 1]

\times [0, 1]

\times R \to K_{c v} (R)

is a given multivalued operator, where

K_{c v}

represents the family of nonempty compact and convex subsets of

R

and

ϖ \in C [0, 1]

is the unknown function. We also provide a non-trivial example to show the significance of our main result. Full article

(This article belongs to the Special Issue Advance in Nonlinear Analysis and Optimization)

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