{"title":"Corrigendum to “WEB-Spline Finite Elements for the Approximation of Navier-Lamé System with \u0000 \u0000 \u0000 C\u0000 \u0000 \u0000 A\u0000 ,\u0000 ","authors":"O. Koubaiti, A. Elkhalfi, J. EL-Mekkaoui","doi":"10.1155/2021/9865431","DOIUrl":"https://doi.org/10.1155/2021/9865431","url":null,"abstract":"<jats:p />","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":"2021 1","pages":"1-1"},"PeriodicalIF":0.0,"publicationDate":"2021-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43416444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper introduces novel concepts of joint ðY , ZÞ cyclic G‐ΩS,T ,ðabef Þ-weak contraction and joint ðY , ZÞ cyclic G‐ΩS,T ,ðabef Þ-weak nonexpansive mappings and then proves the existence of a unique common fixed point of such mappings in case of complete and compact metric spaces, respectively, in particular, it proves the existence of a unique fixed point for both cyclic G‐ΩS,ðabef Þ-weak contraction and cyclic G‐ΩS,ðabef Þ-weak nonexpansive mappings, and hence, it also proves the existence of a unique fixed point for both cyclic ΩS,ðabef Þ-weak contraction and cyclic ΩS,ðabef Þ-weak nonexpansive mappings. The results of this research paper extend and generalize some fixed point theorems previously proved via the attached references.
{"title":"Cyclic \u0000 G\u0000 ‐\u0000 Ω\u0000 -Weak Contraction-Weak Nonexpansive Mappings and Some Fixed Point Theorems in Metric Spaces","authors":"Sahar Mohamed Ali Abou Bakr","doi":"10.1155/2021/6642564","DOIUrl":"https://doi.org/10.1155/2021/6642564","url":null,"abstract":"This paper introduces novel concepts of joint ðY , ZÞ cyclic G‐ΩS,T ,ðabef Þ-weak contraction and joint ðY , ZÞ cyclic G‐ΩS,T ,ðabef Þ-weak nonexpansive mappings and then proves the existence of a unique common fixed point of such mappings in case of complete and compact metric spaces, respectively, in particular, it proves the existence of a unique fixed point for both cyclic G‐ΩS,ðabef Þ-weak contraction and cyclic G‐ΩS,ðabef Þ-weak nonexpansive mappings, and hence, it also proves the existence of a unique fixed point for both cyclic ΩS,ðabef Þ-weak contraction and cyclic ΩS,ðabef Þ-weak nonexpansive mappings. The results of this research paper extend and generalize some fixed point theorems previously proved via the attached references.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":"2021 1","pages":"1-9"},"PeriodicalIF":0.0,"publicationDate":"2021-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47923395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce and study two properties of dynamical systems: topologically transitive and topologically mixing under the set-valued setting. We prove some implications of these two properties for set-valued functions and generalize some results from a single-valued case to a set-valued case. We also show that both properties of set-valued dynamical systems are equivalence for any compact intervals.
{"title":"Topologically Transitive and Mixing Properties of Set-Valued Dynamical Systems","authors":"K. S. Wong, Z. Salleh","doi":"10.1155/2021/5541105","DOIUrl":"https://doi.org/10.1155/2021/5541105","url":null,"abstract":"We introduce and study two properties of dynamical systems: topologically transitive and topologically mixing under the set-valued setting. We prove some implications of these two properties for set-valued functions and generalize some results from a single-valued case to a set-valued case. We also show that both properties of set-valued dynamical systems are equivalence for any compact intervals.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":"2021 1","pages":"1-7"},"PeriodicalIF":0.0,"publicationDate":"2021-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43146844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Frame theory has a great revolution for recent years. This theory has been extended from Hilbert spaces to Hilbert - modules. In this paper, we define and study the new concept of controlled continuous - - - frames for Hilbert - modules and we establish some properties.
{"title":"Controlled Continuous \u0000 ∗\u0000 -\u0000 K\u0000 -\u0000 g\u0000 -Frames for Hilbert \u0000 \u0000 \u0000 C\u0000 \u0000 \u0000 ","authors":"A. Touri, H. Labrigui, M. Rossafi, S. Kabbaj","doi":"10.1155/2021/5548935","DOIUrl":"https://doi.org/10.1155/2021/5548935","url":null,"abstract":"Frame theory has a great revolution for recent years. This theory has been extended from Hilbert spaces to Hilbert - modules. In this paper, we define and study the new concept of controlled continuous - - - frames for Hilbert - modules and we establish some properties.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":"1-11"},"PeriodicalIF":0.0,"publicationDate":"2021-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46524270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we give an equivalent characterization of the Besov space. This reveals the equivalent relation between the mixed derivative norm and single-variable norm. Fourier multiplier, real interpolation, and Littlewood-Paley decomposition are applied.
{"title":"Equivalent Characterization on Besov Space","authors":"Cong He, Jingchun Chen","doi":"10.1155/2021/6688250","DOIUrl":"https://doi.org/10.1155/2021/6688250","url":null,"abstract":"In this paper, we give an equivalent characterization of the Besov space. This reveals the equivalent relation between the mixed derivative norm and single-variable norm. Fourier multiplier, real interpolation, and Littlewood-Paley decomposition are applied.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45998494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Jacobi elliptic function method is applied to solve the generalized Benjamin-Bona-Mahony equation (BBM). Periodic and soliton solutions are formally derived in a general form. Some particular cases are considered. A power series method is also applied in some particular cases. Some solutions are expressed in terms of the Weierstrass elliptic function.
{"title":"New Solutions for the Generalized BBM Equation in terms of Jacobi and Weierstrass Elliptic Functions","authors":"A. Salas, L. Martínez H, D. Ocampo R","doi":"10.1155/2021/5513266","DOIUrl":"https://doi.org/10.1155/2021/5513266","url":null,"abstract":"The Jacobi elliptic function method is applied to solve the generalized Benjamin-Bona-Mahony equation (BBM). Periodic and soliton solutions are formally derived in a general form. Some particular cases are considered. A power series method is also applied in some particular cases. Some solutions are expressed in terms of the Weierstrass elliptic function.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47008924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The aim of this paper is to extend the notion of - Riemann integrability of functions defined over to functions defined over a rectangular box of . As a generalization of step functions, we introduce a notion of - step functions which allows us to give an equivalent definition of the - Riemann integrable functions.
{"title":"The Multiple \u0000 K\u0000 -Riemann Integral","authors":"Oussama Kabbouch, M. Najmeddine","doi":"10.1155/2021/6690328","DOIUrl":"https://doi.org/10.1155/2021/6690328","url":null,"abstract":"The aim of this paper is to extend the notion of - Riemann integrability of functions defined over to functions defined over a rectangular box of . As a generalization of step functions, we introduce a notion of - step functions which allows us to give an equivalent definition of the - Riemann integrable functions.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42185389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abdelkrim Salim, M. Benchohra, J. Lazreg, G. N’Guérékata
This article deals with some existence, uniqueness, and Ulam-Hyers-Rassias stability results for a class of boundary value problem for nonlinear implicit fractional differential equations with impulses and generalized Hilfer Fractional derivative. The results are obtained using the Banach contraction principle and Krasnoselskii’s and Schaefer’s fixed-point theorems.
{"title":"Boundary Value Problem for Nonlinear Implicit Generalized Hilfer-Type Fractional Differential Equations with Impulses","authors":"Abdelkrim Salim, M. Benchohra, J. Lazreg, G. N’Guérékata","doi":"10.1155/2021/5592010","DOIUrl":"https://doi.org/10.1155/2021/5592010","url":null,"abstract":"This article deals with some existence, uniqueness, and Ulam-Hyers-Rassias stability results for a class of boundary value problem for nonlinear implicit fractional differential equations with impulses and generalized Hilfer Fractional derivative. The results are obtained using the Banach contraction principle and Krasnoselskii’s and Schaefer’s fixed-point theorems.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49252037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper is aimed at proving a common fixed point theorem for - Kannan mappings in metric spaces with an application to integral equations. The main result of the paper will extend and generalise the recent existing fixed point results in the literature. We also provided illustrative examples and some applications to integral equation, nonlinear fractional differential equation, and ordinary differential equation for damped forced oscillations to support the results.
{"title":"A Common Fixed Point Theorem for Generalised \u0000 F\u0000 -Kannan Mapping in Metric Space with Applications","authors":"Lucas Wangwe, Santosh Kumar","doi":"10.1155/2021/6619877","DOIUrl":"https://doi.org/10.1155/2021/6619877","url":null,"abstract":"This paper is aimed at proving a common fixed point theorem for - Kannan mappings in metric spaces with an application to integral equations. The main result of the paper will extend and generalise the recent existing fixed point results in the literature. We also provided illustrative examples and some applications to integral equation, nonlinear fractional differential equation, and ordinary differential equation for damped forced oscillations to support the results.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":"2021 1","pages":"1-12"},"PeriodicalIF":0.0,"publicationDate":"2021-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44723126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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