Abstract and Applied Analysis最新文献

{"title":"Simultaneous Developability of Partner Ruled Surfaces according to Darboux Frame in \u0000 \u0000 \u0000 E\u0000 \u0000 \u0000 3","authors":"Soukaina Ouarab","doi":"10.1155/2021/3151501","DOIUrl":"https://doi.org/10.1155/2021/3151501","url":null,"abstract":"<jats:p>In this paper, we introduce original definitions of Partner ruled surfaces according to the Darboux frame of a curve lying on an arbitrary regular surface in <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <msup>\u0000 <mrow>\u0000 <mi>E</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 </msup>\u0000 </math>\u0000 </jats:inline-formula>. It concerns <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <mi>T</mi>\u0000 <mi>g</mi>\u0000 </math>\u0000 </jats:inline-formula> Partner ruled surfaces, <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <mi>T</mi>\u0000 <mi>n</mi>\u0000 </math>\u0000 </jats:inline-formula> Partner ruled surfaces, and <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\u0000 <mi>g</mi>\u0000 <mi>n</mi>\u0000 </math>\u0000 </jats:inline-formula> Partner ruled surfaces. We aim to study the simultaneous developability conditions of each couple of two Partner ruled surfaces. Finally, we give an illustrative example for our study.</jats:p>","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47859838","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}

{"title":"On Two Banach-Type Fixed Points in Bipolar Metric Spaces","authors":"Yaé Ulrich Gaba, M. Aphane, V. Sihag","doi":"10.1155/2021/4846877","DOIUrl":"https://doi.org/10.1155/2021/4846877","url":null,"abstract":"In this article, we propose two Banach-type fixed point theorems on bipolar metric spaces. More specifically, we look at covariant maps between bipolar metric spaces and consider iterates of the map involved. We also propose a generalization of the Banach fixed point result via Caristi-type arguments.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42180313","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}

{"title":"The Marichev-Saigo-Maeda Fractional Calculus Operators Pertaining to the \u0000 V\u0000 -Function","authors":"S. Chandak, Biniyam Shimelis, Nigussie Abeye, A. Padma","doi":"10.1155/2021/9961013","DOIUrl":"https://doi.org/10.1155/2021/9961013","url":null,"abstract":"In the present paper, we establish some composition formulas for Marichev-Saigo-Maeda (MSM) fractional calculus operators with \u0000 \u0000 V\u0000 \u0000 -function as the kernel. In addition, on account of \u0000 \u0000 V\u0000 \u0000 -function, a variety of known results associated with special functions such as the Mittag-Leffler function, exponential function, Struve’s function, Lommel’s function, the Bessel function, Wright’s generalized Bessel function, and the generalized hypergeometric function have been discovered by defining suitable values for the parameters.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47163348","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}

{"title":"On Solitary Wave Solutions for the Camassa-Holm and the Rosenau-RLW-Kawahara Equations with the Dual-Power Law Nonlinearities","authors":"N. Sukantamala, Supawan Nanta","doi":"10.1155/2021/6649285","DOIUrl":"https://doi.org/10.1155/2021/6649285","url":null,"abstract":"The nonlinear wave equation is a significant concern to describe wave behavior and structures. Various mathematical models related to the wave phenomenon have been introduced and extensively being studied due to the complexity of wave behaviors. In the present work, a mathematical model to obtain the solution of the nonlinear wave by coupling the classical Camassa-Holm equation and the Rosenau-RLW-Kawahara equation with the dual term of nonlinearities is proposed. The solution properties are analytically derived. The new model still satisfies the fundamental energy conservative property as the original models. We then apply the energy method to prove the well-posedness of the model under the solitary wave hypothesis. Some categories of exact solitary wave solutions of the model are described by using the Ansatz method. In addition, we found that the dual term of nonlinearity is essential to obtain the class of analytic solution. Besides, we provide some graphical representations to illustrate the behavior of the traveling wave solutions.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47823919","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}

{"title":"The Product-Type Operators from Hardy Spaces into \u0000 n\u0000 th Weighted-Type Spaces","authors":"Ebrahim Abbasi","doi":"10.1155/2021/5556275","DOIUrl":"https://doi.org/10.1155/2021/5556275","url":null,"abstract":"<jats:p>The main goal of this paper is to investigate the boundedness and essential norm of a class of product-type operators <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <msubsup>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>u</mi>\u0000 <mo>,</mo>\u0000 <mi>v</mi>\u0000 <mo>,</mo>\u0000 <mi>φ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 </msubsup>\u0000 <mo>,</mo>\u0000 <mi>m</mi>\u0000 <mo>∈</mo>\u0000 <mi>ℕ</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> from Hardy spaces into <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <mi>n</mi>\u0000 </math>\u0000 </jats:inline-formula>th weighted-type spaces. As a corollary, we obtain some equivalent conditions for compactness of such operators.</jats:p>","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45129707","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}

{"title":"Projections in Moduli Spaces of the Kleinian Groups","authors":"Hala Alaqad, J. Gong, G. Martin","doi":"10.1155/2022/6311193","DOIUrl":"https://doi.org/10.1155/2022/6311193","url":null,"abstract":"<jats:p>A two-generator Kleinian group <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mfenced open=\"〈\" close=\"〉\">\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>,</mo>\u0000 <mi>g</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> can be naturally associated with a discrete group <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mfenced open=\"〈\" close=\"〉\">\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>,</mo>\u0000 <mi>ϕ</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> with the generator <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <mi>ϕ</mi>\u0000 </math>\u0000 </jats:inline-formula> of order two and where <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <mfenced open=\"〈\" close=\"〉\">\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>,</mo>\u0000 <mi>ϕ</mi>\u0000 <mi>f</mi>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ϕ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 </mfenced>\u0000 <mo>=</mo>\u0000 <mfenced open=\"〈\" close=\"〉\">\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>,</mo>\u0000 <mi>g</mi>\u0000 <mi>f</mi>\u0000 <msup>\u0000 <mrow>\u0000 <mi>g</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 </mfenced>\u0000 <mo>⊂</mo>\u0000 <mfenced open=\"〈\" close=\"〉\">\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>,</mo>\u0000 ","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44360193","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}

{"title":"Small Modification on Modified Euler Method for Solving Initial Value Problems","authors":"Abushet Hayalu Workie","doi":"10.1155/2021/9951815","DOIUrl":"https://doi.org/10.1155/2021/9951815","url":null,"abstract":"In this article, small modification to the Modified Euler Method is proposed. Stability and consistency were tested to determine the end result, and some numerical results were presented, and the CPU time was compared again, and it is recognized that the proposed method is more reliable and compatible with higher efficiency.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43223606","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}

{"title":"Fitted Numerical Scheme for Second-Order Singularly Perturbed Differential-Difference Equations with Mixed Shifts","authors":"Meku Ayalew, G. G. Kiltu, G. Duressa","doi":"10.1155/2021/4573847","DOIUrl":"https://doi.org/10.1155/2021/4573847","url":null,"abstract":"This paper presents the study of singularly perturbed differential-difference equations of delay and advance parameters. The proposed numerical scheme is a fitted fourth-order finite difference approximation for the singularly perturbed differential equations at the nodal points and obtained a tridiagonal scheme. This is significant because the proposed method is applicable for the perturbation parameter which is less than the mesh size\u0000 \u0000 ,\u0000 \u0000 where most numerical methods fail to give good results. Moreover, the work can also help to introduce the technique of establishing and making analysis for the stability and convergence of the proposed numerical method, which is the crucial part of the numerical analysis. Maximum absolute errors range from \u0000 \u0000 \u0000 \u0000 10\u0000 \u0000 \u0000 −\u0000 03\u0000 \u0000 \u0000 \u0000 up to \u0000 \u0000 \u0000 \u0000 10\u0000 \u0000 \u0000 −\u0000 10\u0000 \u0000 \u0000 \u0000 , and computational rate of convergence for different values of perturbation parameter, delay and advance parameters, and mesh sizes are tabulated for the considered numerical examples. Concisely, the present method is stable and convergent and gives more accurate results than some existing numerical methods reported in the literature.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45635446","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}

{"title":"An Extension of the Carathéodory Differentiability to Set-Valued Maps","authors":"Pedro Hurtado, Alexander Leones, M. Martelo, J. Moreno","doi":"10.1155/2021/5529796","DOIUrl":"https://doi.org/10.1155/2021/5529796","url":null,"abstract":"This paper uses the generalization of the Hukuhara difference for compact convex set to extend the classical notions of Caratheodory differentiability to multifunctions (set-valued maps). Using the Hukuhara difference and affine multifunctions as a local approximation, we introduce the notion of CH-differentiability for multifunctions. Finally, we tackle the study of the relation among the Frechet differentiability, Hukuhara differentiability, and CH-differentiability.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":"1-8"},"PeriodicalIF":0.0,"publicationDate":"2021-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48163141","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}

{"title":"Generalized Refinement of Gauss-Seidel Method for Consistently Ordered 2-Cyclic Matrices","authors":"Gashaye Dessalew, T. Kebede, Gurju Awgichew, Assaye Walelign","doi":"10.1155/2021/8343207","DOIUrl":"https://doi.org/10.1155/2021/8343207","url":null,"abstract":"This paper presents generalized refinement of Gauss-Seidel method of solving system of linear equations by considering consistently ordered 2-cyclic matrices. Consistently ordered 2-cyclic matrices are obtained while finite difference method is applied to solve differential equation. Suitable theorems are introduced to verify the convergence of this proposed method. To observe the effectiveness of this method, few numerical examples are given. The study points out that, using the generalized refinement of Gauss-Seidel method, we obtain a solution of a problem with a minimum number of iteration and obtain a greater rate of convergence than other previous methods.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":"1-7"},"PeriodicalIF":0.0,"publicationDate":"2021-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44336032","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}