This paper proves a common fixed point theorem for single-valued and multivalued mappings by using ternary relation in G -metric spaces. Henceforth, results obtained will be verified with the help of illustrative examples. Also, we demonstrate the results with an application.
{"title":"Common Fixed Point Theorem for Multivalued Mappings Using Ternary Relation in \u0000 G\u0000 -Metric Space with an Application","authors":"Lucas Wangwe","doi":"10.1155/2022/3593697","DOIUrl":"https://doi.org/10.1155/2022/3593697","url":null,"abstract":"This paper proves a common fixed point theorem for single-valued and multivalued mappings by using ternary relation in \u0000 \u0000 G\u0000 \u0000 -metric spaces. Henceforth, results obtained will be verified with the help of illustrative examples. Also, we demonstrate the results with an application.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47296192","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 consider a JS metric space endowed with convexity structure, which will allow us to examine and study convergence of Mann iteration and Ishikawa iteration for Banach type and Chatterjea type contractions defined on JS metric space.
{"title":"Convergence of Mann and Ishikawa Iterative Processes for Some Contractions in Convex Generalized Metric Space","authors":"Youness El Kouch, J. Mouline","doi":"10.1155/2022/3168414","DOIUrl":"https://doi.org/10.1155/2022/3168414","url":null,"abstract":"In this paper, we consider a JS metric space endowed with convexity structure, which will allow us to examine and study convergence of Mann iteration and Ishikawa iteration for Banach type and Chatterjea type contractions defined on JS metric space.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45362857","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}
Based on the concept of pseudocomplement, we introduce a new representation of preopenness of -fuzzy sets in -fuzzy bitopological spaces. The concepts of pairwise -fuzzy precontinuous and pairwise -fuzzy preirresolute functions are extended and discussed based on the --preopen gradation. Further, we follow up with a study of pairwise -fuzzy precompactness in -fuzzy bitopological spaces of an -fuzzy set. We find that our paper offers more general results since
{"title":"Preopenness Degree in \u0000 R\u0000 L\u0000 -Fuzzy Bitopological Spaces","authors":"O. H. Khalil, K. E. El-Helow, A. Ghareeb","doi":"10.1155/2022/9210694","DOIUrl":"https://doi.org/10.1155/2022/9210694","url":null,"abstract":"<jats:p>Based on the concept of pseudocomplement, we introduce a new representation of preopenness of <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mi>L</mi>\u0000 </math>\u0000 </jats:inline-formula>-fuzzy sets in <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <mi>R</mi>\u0000 <mi>L</mi>\u0000 </math>\u0000 </jats:inline-formula>-fuzzy bitopological spaces. The concepts of pairwise <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <mi>R</mi>\u0000 <mi>L</mi>\u0000 </math>\u0000 </jats:inline-formula>-fuzzy precontinuous and pairwise <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\u0000 <mi>R</mi>\u0000 <mi>L</mi>\u0000 </math>\u0000 </jats:inline-formula>-fuzzy preirresolute functions are extended and discussed based on the <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\">\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>i</mi>\u0000 <mo>,</mo>\u0000 <mi>j</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula>-<jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M7\">\u0000 <mi>R</mi>\u0000 <mi>L</mi>\u0000 </math>\u0000 </jats:inline-formula>-preopen gradation. Further, we follow up with a study of pairwise <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M8\">\u0000 <mi>R</mi>\u0000 <mi>L</mi>\u0000 </math>\u0000 </jats:inline-formula>-fuzzy precompactness in <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M9\">\u0000 <mi>R</mi>\u0000 <mi>L</mi>\u0000 </math>\u0000 </jats:inline-formula>-fuzzy bitopological spaces of an <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M10\">\u0000 <mi>L</mi>\u0000 </math>\u0000 </jats:inline-formula>-fuzzy set. We find that our paper offers more general results since <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M11\">\u0000 <mi>R</mi>\u0000 <mi>L</mi>\u0000 </math>\u0000 </jats:i","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41721428","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 show that in order for a proper compact subset of plane to be convex, it is necessary and sufficient that inverse norm function be subharmonic.
在本文中，我们证明了对于平面的适当紧子集Kℝ 2是凸的，逆范数函数是次调和的是必要的，也是充分的。
{"title":"Convex Sets and Subharmonicity of the Inverse Norm Function","authors":"M. Heydari","doi":"10.1155/2022/1172007","DOIUrl":"https://doi.org/10.1155/2022/1172007","url":null,"abstract":"<jats:p>In this paper, we show that in order for a proper compact subset <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mi>K</mi>\u0000 </math>\u0000 </jats:inline-formula> of plane <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </math>\u0000 </jats:inline-formula> to be convex, it is necessary and sufficient that inverse norm function be subharmonic.</jats:p>","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49350098","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 Bishop frame or rotation minimizing frame (RMF) is an alternative approach to define a moving frame that is well defined even when the curve has vanished second derivative, and it has been widely used in the areas of computer graphics, engineering, and biology. The main aim of this paper is using the RMF for classification of singularity type of timelike sweeping surface and Bishop spherical Darboux image which is mightily concerning a unit speed spacelike curve with timelike binormal vector in E 1 3 .
{"title":"On the Timelike Sweeping Surfaces and Singularities in Minkowski 3-Space \u0000 \u0000 \u0000 E\u0000 \u0000 \u0000 1\u0000 \u0000 \u0000 ","authors":"N. Alluhaibi, R. Abdel-Baky, Monia Naghi","doi":"10.1155/2022/9121239","DOIUrl":"https://doi.org/10.1155/2022/9121239","url":null,"abstract":"The Bishop frame or rotation minimizing frame (RMF) is an alternative approach to define a moving frame that is well defined even when the curve has vanished second derivative, and it has been widely used in the areas of computer graphics, engineering, and biology. The main aim of this paper is using the RMF for classification of singularity type of timelike sweeping surface and Bishop spherical Darboux image which is mightily concerning a unit speed spacelike curve with timelike binormal vector in \u0000 \u0000 \u0000 \u0000 E\u0000 \u0000 \u0000 1\u0000 \u0000 \u0000 3\u0000 \u0000 \u0000 \u0000 .","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47833330","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 first introduce two new notions of uniform convexity on a geodesic space, and we prove their properties. Moreover, we reintroduce a concept of the set-convergence in complete geodesic spaces, and we prove a relation between the metric projections and the convergence of a sequence of sets.
{"title":"Uniform Convexity and Convergence of a Sequence of Sets in a Complete Geodesic Space","authors":"Y. Kimura, Shuta Sudo","doi":"10.1155/2022/9534978","DOIUrl":"https://doi.org/10.1155/2022/9534978","url":null,"abstract":"In this paper, we first introduce two new notions of uniform convexity on a geodesic space, and we prove their properties. Moreover, we reintroduce a concept of the set-convergence in complete geodesic spaces, and we prove a relation between the metric projections and the convergence of a sequence of sets.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47099350","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, the dynamical behavior of a three-dimensional fractional-order prey-predator model is investigated with Holling type III functional response and constant rate harvesting. It is assumed that the middle predator species consumes only the prey species, and the top predator species consumes only the middle predator species. We also prove the boundedness, the non-negativity, the uniqueness, and the existence of the solutions of the proposed model. Then, all possible equilibria are determined, and the dynamical behaviors of the proposed model around the equilibrium points are investigated. Finally, numerical simulations results are presented to confirm the theoretical results and to give a better understanding of the dynamics of our proposed model.
{"title":"Dynamical Behaviors of a Fractional-Order Three Dimensional Prey-Predator Model","authors":"Noor S. Sh. Barhoom, Sadiq Al-Nassir","doi":"10.1155/2021/1366797","DOIUrl":"https://doi.org/10.1155/2021/1366797","url":null,"abstract":"In this paper, the dynamical behavior of a three-dimensional fractional-order prey-predator model is investigated with Holling type III functional response and constant rate harvesting. It is assumed that the middle predator species consumes only the prey species, and the top predator species consumes only the middle predator species. We also prove the boundedness, the non-negativity, the uniqueness, and the existence of the solutions of the proposed model. Then, all possible equilibria are determined, and the dynamical behaviors of the proposed model around the equilibrium points are investigated. Finally, numerical simulations results are presented to confirm the theoretical results and to give a better understanding of the dynamics of our proposed model.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48225418","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, weighted norm inequalities for multilinear Fourier multipliers satisfying Sobolev regularity with mixed norm are discussed. Our result can be understood as a generalization of the result by Fujita and Tomita by using the -based Sobolev space, with mixed norm.
{"title":"Weighted Norm Inequalities for Multilinear Fourier Multipliers with Mixed Norm","authors":"Mai Fujita","doi":"10.1155/2021/8289155","DOIUrl":"https://doi.org/10.1155/2021/8289155","url":null,"abstract":"<jats:p>In this paper, weighted norm inequalities for multilinear Fourier multipliers satisfying Sobolev regularity with mixed norm are discussed. Our result can be understood as a generalization of the result by Fujita and Tomita by using the <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <msup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 </msup>\u0000 </math>\u0000 </jats:inline-formula>-based Sobolev space, <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mn>1</mn>\u0000 <mo><</mo>\u0000 <mi>r</mi>\u0000 <mo>≤</mo>\u0000 <mn>2</mn>\u0000 </math>\u0000 </jats:inline-formula> with mixed norm.</jats:p>","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44497524","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 investigation of the numerical solution of the laminar boundary layer flow along with a moving cylinder with heat generation, thermal radiation, and surface slip effect is carried out. The fluid mathematical model developed from the Navier-Stokes equations resulted in a system of partial differential equations which were then solved by the multidomain bivariate spectral quasilinearization method (MD-BSQLM). The results show that increasing the velocity slip factor results in an enhanced increase in velocity and temperature profiles. Increasing the heat generation parameter increases temperature profiles; increasing the radiation parameter and the Eckert numbers both increase the temperature profiles. The concentration profiles decrease with increasing radial coordinate. Increasing the Brownian motion and the thermophoresis parameter both destabilizes the concentration profiles. Increasing the Schmidt number reduces temperature profiles. The effect of increasing selected parameters: the velocity slip, Brownian motion, and the radiation parameter on all residual errors show that these errors do not deteriorate. This shows that the MD-BSQLM is very accurate and robust. The method was compared with similar results in the literature and was found to be in excellent agreement.
{"title":"Numerical Solutions for Laminar Boundary Layer Nanofluid Flow along with a Moving Cylinder with Heat Generation, Thermal Radiation, and Slip Parameter","authors":"T. M. Agbaje, G. Makanda","doi":"10.1155/2021/8288534","DOIUrl":"https://doi.org/10.1155/2021/8288534","url":null,"abstract":"The investigation of the numerical solution of the laminar boundary layer flow along with a moving cylinder with heat generation, thermal radiation, and surface slip effect is carried out. The fluid mathematical model developed from the Navier-Stokes equations resulted in a system of partial differential equations which were then solved by the multidomain bivariate spectral quasilinearization method (MD-BSQLM). The results show that increasing the velocity slip factor results in an enhanced increase in velocity and temperature profiles. Increasing the heat generation parameter increases temperature profiles; increasing the radiation parameter and the Eckert numbers both increase the temperature profiles. The concentration profiles decrease with increasing radial coordinate. Increasing the Brownian motion and the thermophoresis parameter both destabilizes the concentration profiles. Increasing the Schmidt number reduces temperature profiles. The effect of increasing selected parameters: the velocity slip, Brownian motion, and the radiation parameter on all residual errors show that these errors do not deteriorate. This shows that the MD-BSQLM is very accurate and robust. The method was compared with similar results in the literature and was found to be in excellent agreement.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46509374","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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