Pub Date : 2021-06-26DOI: 10.46753/pjaa.2021.v08i01(i).015
{"title":"DECOMPOSITION OF δ-CONTINUITY VIA e-OPEN SET","authors":"","doi":"10.46753/pjaa.2021.v08i01(i).015","DOIUrl":"https://doi.org/10.46753/pjaa.2021.v08i01(i).015","url":null,"abstract":"","PeriodicalId":37079,"journal":{"name":"Poincare Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44476862","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}
Pub Date : 2021-06-26DOI: 10.46753/pjaa.2021.v08i01(i).006
{"title":"ON CONTRA we*-CONTINUOUS FUNCTIONS","authors":"","doi":"10.46753/pjaa.2021.v08i01(i).006","DOIUrl":"https://doi.org/10.46753/pjaa.2021.v08i01(i).006","url":null,"abstract":"","PeriodicalId":37079,"journal":{"name":"Poincare Journal of Analysis and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41791459","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}
Pub Date : 2021-02-18DOI: 10.33786/pjaa.2021.v08i01(i).011
A. Pigazzini, C. Ozel, P. Linker, S. Jafari
We provide a possible way of constructing new kinds of manifolds which we will call Partially Negative Dimensional Product manifold (PNDP-manifold for short). In particular a PNDP-manifold is an Einstein warped product manifold of special kind, where the base-manifold $B$ is a Remannian (or pseudo-Riemannian) product-manifold $B=Pi_{i=1}^{q'}B_i times Pi_{i=(q'+1)}^{widetilde q} B_i$, with $Pi_{i=(q'+1)}^{widetilde q} B_i$ an Einstein-manifold, and the fiber-manifold $F$ is a derived-differential-manifold (i.e., $F$ is the form: smooth manifold ($mathbb{R}^d$)+ obstruction bundle, so it can admit negative dimension). Since the dimension of a PNDP-manifold is not related with the usual geometric concept of dimension, from the speculative and applicative point of view, we try to define this relation using the concept of desuspension to identify the PNDP with another kind of"object", introducing a new kind of hidden dimensions.
{"title":"ON PNDP-MANIFOLD","authors":"A. Pigazzini, C. Ozel, P. Linker, S. Jafari","doi":"10.33786/pjaa.2021.v08i01(i).011","DOIUrl":"https://doi.org/10.33786/pjaa.2021.v08i01(i).011","url":null,"abstract":"We provide a possible way of constructing new kinds of manifolds which we will call Partially Negative Dimensional Product manifold (PNDP-manifold for short). In particular a PNDP-manifold is an Einstein warped product manifold of special kind, where the base-manifold $B$ is a Remannian (or pseudo-Riemannian) product-manifold $B=Pi_{i=1}^{q'}B_i times Pi_{i=(q'+1)}^{widetilde q} B_i$, with $Pi_{i=(q'+1)}^{widetilde q} B_i$ an Einstein-manifold, and the fiber-manifold $F$ is a derived-differential-manifold (i.e., $F$ is the form: smooth manifold ($mathbb{R}^d$)+ obstruction bundle, so it can admit negative dimension). Since the dimension of a PNDP-manifold is not related with the usual geometric concept of dimension, from the speculative and applicative point of view, we try to define this relation using the concept of desuspension to identify the PNDP with another kind of\"object\", introducing a new kind of hidden dimensions.","PeriodicalId":37079,"journal":{"name":"Poincare Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47298694","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}
Pub Date : 2020-12-30DOI: 10.46753/pjaa.2020.v07i02.006
T. Khan, H. Chaudhary
This research addresses a systematic design for investigating hybrid projective combination difference synchronization (HPCDS) scheme between chaotic prey-predator systems via active control method. The presented work deals with generalized Lotka and Volterra (GLV) biological system. The considered system analyzes the interactions among three species prey (one) and predators (two) that comprises of a system of ordinary differential equations. An active control approach has been investigated which is primarily based on Lyapunov stability theory (LST). The discussed scheme derives the asymptotic stability globally using HPCDS technique. Numerical simulations are thereafter implemented to validate the efficiency and feasibility of the discussed strategy using MATLAB. Interestingly, both the computational and theoretical results agree remarkably. In addition, a comparison analysis has been done which shows the significance of considered approach over prior published researches. Furthermore, the considered HPCDS scheme is useful in secure communication and encrypting images.
{"title":"An investigation on hybrid projective combination difference synchronization scheme between chaotic prey-predator systems via active control method","authors":"T. Khan, H. Chaudhary","doi":"10.46753/pjaa.2020.v07i02.006","DOIUrl":"https://doi.org/10.46753/pjaa.2020.v07i02.006","url":null,"abstract":"This research addresses a systematic design for investigating hybrid projective combination difference synchronization (HPCDS) scheme between chaotic prey-predator systems via active control method. The presented work deals with generalized Lotka and Volterra (GLV) biological system. The considered system analyzes the interactions among three species prey (one) and predators (two) that comprises of a system of ordinary differential equations. An active control approach has been investigated which is primarily based on Lyapunov stability theory (LST). The discussed scheme derives the asymptotic stability globally using HPCDS technique. Numerical simulations are thereafter implemented to validate the efficiency and feasibility of the discussed strategy using MATLAB. Interestingly, both the computational and theoretical results agree remarkably. In addition, a comparison analysis has been done which shows the significance of considered approach over prior published researches. Furthermore, the considered HPCDS scheme is useful in secure communication and encrypting images.","PeriodicalId":37079,"journal":{"name":"Poincare Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46049550","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}
Pub Date : 2020-12-30DOI: 10.46753/pjaa.2020.v07i02.008
D. Kiran, M. Kameswari
In this paper, we obtain common fixed points for two self maps satisfying a general rational contraction conditions in the frame work of extended rectangular B-metric spaces. In order to justify our results, we have provided some examples. Our results improve and extend the results of Alqahtani et al. [2] and Asim et al. [3]. We apply our results to examine the existence of common fixed points in extended rectangular B-metric spaces equipped with a directed graph.
在扩展的矩形b -度量空间框架中，我们得到了满足一般有理收缩条件的两个自映射的公共不动点。为了证明我们的结果，我们提供了一些例子。我们的结果改进并扩展了Alqahtani et al.[2]和Asim et al.[3]的结果。我们应用我们的结果来检验具有有向图的扩展矩形b -度量空间中公共不动点的存在性。
{"title":"Common fixed points of a pair of generalized rational contraction maps in extended rectangular B-metric spaces","authors":"D. Kiran, M. Kameswari","doi":"10.46753/pjaa.2020.v07i02.008","DOIUrl":"https://doi.org/10.46753/pjaa.2020.v07i02.008","url":null,"abstract":"In this paper, we obtain common fixed points for two self maps satisfying a general rational contraction conditions in the frame work of extended rectangular B-metric spaces. In order to justify our results, we have provided some examples. Our results improve and extend the results of Alqahtani et al. [2] and Asim et al. [3]. We apply our results to examine the existence of common fixed points in extended rectangular B-metric spaces equipped with a directed graph.","PeriodicalId":37079,"journal":{"name":"Poincare Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45719574","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}
Pub Date : 2020-12-30DOI: 10.46753/pjaa.2020.v07i02.010
Narendra N. Jha, Shalu Sharma
Abstract. In this note, we introduce block sequences for a retro Banach frame and exhibit the existence with examples and counter examples. Also, we give a necessary and sufficient condition for a block sequence of a retro Banach frame to be a retro Banach frame. We give a condition (a necessary and sufficient) under which a block sequence of an exact retro Banach frame is an exact retro Banach frame. Finally, we discuss exact retro Banach frames and prove a result related to a geometric property of the underlying space.
{"title":"Block sequences of Retro Banach Frames","authors":"Narendra N. Jha, Shalu Sharma","doi":"10.46753/pjaa.2020.v07i02.010","DOIUrl":"https://doi.org/10.46753/pjaa.2020.v07i02.010","url":null,"abstract":"Abstract. In this note, we introduce block sequences for a retro Banach frame and exhibit the existence with examples and counter examples. Also, we give a necessary and sufficient condition for a block sequence of a retro Banach frame to be a retro Banach frame. We give a condition (a necessary and sufficient) under which a block sequence of an exact retro Banach frame is an exact retro Banach frame. Finally, we discuss exact retro Banach frames and prove a result related to a geometric property of the underlying space.","PeriodicalId":37079,"journal":{"name":"Poincare Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42242506","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}
Pub Date : 2020-12-30DOI: 10.46753/pjaa.2020.v07i02.007
Debasis Sharma, S. K. Parhi, S. K. Sunanda
In this paper, we provide an improved local analysis of deformed Halley method using Hölder continuous first-order Fréchet derivative in Banach spaces. This analysis avoids the use of the extra assumption on the boundedness of the first derivative. Finally, numerical applications confirm that our analysis provides larger convergence radii in comparison with the earlier study.
{"title":"An improved local analysis of deformed Halley method in Banach spaces","authors":"Debasis Sharma, S. K. Parhi, S. K. Sunanda","doi":"10.46753/pjaa.2020.v07i02.007","DOIUrl":"https://doi.org/10.46753/pjaa.2020.v07i02.007","url":null,"abstract":"In this paper, we provide an improved local analysis of deformed Halley method using Hölder continuous first-order Fréchet derivative in Banach spaces. This analysis avoids the use of the extra assumption on the boundedness of the first derivative. Finally, numerical applications confirm that our analysis provides larger convergence radii in comparison with the earlier study.","PeriodicalId":37079,"journal":{"name":"Poincare Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43517952","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}
Pub Date : 2020-12-30DOI: 10.46753/pjaa.2020.v07i02.004
D. C. Pereira, C. Raposo, C. Maranhão, A. Cattai
{"title":"Wave coupled system of the $p$-Laplacian type","authors":"D. C. Pereira, C. Raposo, C. Maranhão, A. Cattai","doi":"10.46753/pjaa.2020.v07i02.004","DOIUrl":"https://doi.org/10.46753/pjaa.2020.v07i02.004","url":null,"abstract":"","PeriodicalId":37079,"journal":{"name":"Poincare Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42760965","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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