Pub Date : 2023-06-30DOI: 10.46753/pjaa.2023.v010i01.011
R. Ramesh, A. Al-Omari
{"title":"DECOMPOSITION OF (α-H_σ,λ)-CONTINUITY","authors":"R. Ramesh, A. Al-Omari","doi":"10.46753/pjaa.2023.v010i01.011","DOIUrl":"https://doi.org/10.46753/pjaa.2023.v010i01.011","url":null,"abstract":"","PeriodicalId":37079,"journal":{"name":"Poincare Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46814996","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 : 2023-06-30DOI: 10.46753/pjaa.2023.v010i01.005
M. Devi, Seema Sharma, Sunil Rawan
. In this article, a general procedure of forming the Haar wavelets operational matrix is discussed. The Haar wavelet system which has localization property is applied to find approximate solution to a given system which is very near to the exact solution of the system. We demonstrate this procedure through numerical examples. A comparison of approximate solutions and the exact solutions is done along with the error analysis in order to establish that the Haar wavelet system gives better approximate solutions.
{"title":"NUMERICAL SOLUTIONS OF SYSTEM OF LINEAR DIFFERENTIAL EQUATIONS USING HAAR WAVELET APPROACH","authors":"M. Devi, Seema Sharma, Sunil Rawan","doi":"10.46753/pjaa.2023.v010i01.005","DOIUrl":"https://doi.org/10.46753/pjaa.2023.v010i01.005","url":null,"abstract":". In this article, a general procedure of forming the Haar wavelets operational matrix is discussed. The Haar wavelet system which has localization property is applied to find approximate solution to a given system which is very near to the exact solution of the system. We demonstrate this procedure through numerical examples. A comparison of approximate solutions and the exact solutions is done along with the error analysis in order to establish that the Haar wavelet system gives better approximate solutions.","PeriodicalId":37079,"journal":{"name":"Poincare Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44688861","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 : 2023-06-30DOI: 10.46753/pjaa.2023.v010i01.008
K. S. Charak, Rahul Kumar
. In this paper, besides a counterexample to Bloch’s principle, normality criteria leading to counterexamples to the converse of Bloch’s principle in several complex variables are proved. Some Picard-type theorems and their corresponding normality criteria in C n are also obtained.
{"title":"SOME PICARD TYPE THEOREMS AND CORRESPONDING NORMALITY CRITERIA IN SEVERAL COMPLEX VARIABLES","authors":"K. S. Charak, Rahul Kumar","doi":"10.46753/pjaa.2023.v010i01.008","DOIUrl":"https://doi.org/10.46753/pjaa.2023.v010i01.008","url":null,"abstract":". In this paper, besides a counterexample to Bloch’s principle, normality criteria leading to counterexamples to the converse of Bloch’s principle in several complex variables are proved. Some Picard-type theorems and their corresponding normality criteria in C n are also obtained.","PeriodicalId":37079,"journal":{"name":"Poincare Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46900708","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 : 2023-06-30DOI: 10.46753/pjaa.2023.v010i01.007
H. Khelifi, Y. El hadfi, Rayan Ikram Addoun
. The present paper aims to study of the Dirichlet problem for a nonlinear degenerate elliptic equation with singular gradient lower order term, we establish existence and regularity estimates for weak solutions of p-Laplacian type elliptic equations of the form {
{"title":"NONLINEAR DEGENERATE p-LAPLACIAN ELLIPTIC EQUATIONS WITH SINGULAR GRADIENT LOWER ORDER TERM","authors":"H. Khelifi, Y. El hadfi, Rayan Ikram Addoun","doi":"10.46753/pjaa.2023.v010i01.007","DOIUrl":"https://doi.org/10.46753/pjaa.2023.v010i01.007","url":null,"abstract":". The present paper aims to study of the Dirichlet problem for a nonlinear degenerate elliptic equation with singular gradient lower order term, we establish existence and regularity estimates for weak solutions of p-Laplacian type elliptic equations of the form {","PeriodicalId":37079,"journal":{"name":"Poincare Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44328642","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 : 2023-06-30DOI: 10.46753/pjaa.2023.v010i01.009
S. Sharma, Nitin Sharma, K. Poumai
. In [26] authors have defined and studied K -fusion frames in Hilbert spaces. Motivated by [26], we define K -fusion frames in Quaternionic Hilbert spaces and study their perturbations. Further, we define the woven K -fusion frames in Quaternionic Hilbert spaces. Finally, we study the Paley-Wiener type perturbation for weaving K -fusion frames in quaternionic Hilbert spaces.
{"title":"K-FUSION FRAMES IN QUATERNIONIC HILBERT SPACES","authors":"S. Sharma, Nitin Sharma, K. Poumai","doi":"10.46753/pjaa.2023.v010i01.009","DOIUrl":"https://doi.org/10.46753/pjaa.2023.v010i01.009","url":null,"abstract":". In [26] authors have defined and studied K -fusion frames in Hilbert spaces. Motivated by [26], we define K -fusion frames in Quaternionic Hilbert spaces and study their perturbations. Further, we define the woven K -fusion frames in Quaternionic Hilbert spaces. Finally, we study the Paley-Wiener type perturbation for weaving K -fusion frames in quaternionic Hilbert spaces.","PeriodicalId":37079,"journal":{"name":"Poincare Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47952491","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 : 2023-06-30DOI: 10.46753/pjaa.2023.v010i01.012
Manoj Pankaj, †. Kumar, And Vinit Mor
. In this manuscript, we shall introduce hybrid contractions and prove fixed point theorems for such contractions in metric-like spaces. Some existing results of literature shall also be deduced from our main results. We shall provide an example to support the main result. In the end, a fractional integral equation shall also be solved using our main result.
{"title":"SOLUTION OF FRACTIONAL INTEGRAL EQUATION VIA HYBRID CONTRACTIONS IN METRIC-LIKE SPACES","authors":"Manoj Pankaj, †. Kumar, And Vinit Mor","doi":"10.46753/pjaa.2023.v010i01.012","DOIUrl":"https://doi.org/10.46753/pjaa.2023.v010i01.012","url":null,"abstract":". In this manuscript, we shall introduce hybrid contractions and prove fixed point theorems for such contractions in metric-like spaces. Some existing results of literature shall also be deduced from our main results. We shall provide an example to support the main result. In the end, a fractional integral equation shall also be solved using our main result.","PeriodicalId":37079,"journal":{"name":"Poincare Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46329340","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 : 2023-06-30DOI: 10.46753/pjaa.2023.v010i01.015
Raksha Sharma
. In quantum mechanics, a Hilbert space administer a structure (linear) for physical states and also provide an inner product to convey physically-measurable expectation values. Keeping this aspect in mind, in this paper, we prove some significant properties concerning operator valued frames (OPV-frames). Also, we construct OPV-frames with the help of some given operators. Finally, we consider perturbation of OPV-frames and discuss the stability of OPV-frames.
{"title":"SOME PROPERTIES OF OPV-FRAMES","authors":"Raksha Sharma","doi":"10.46753/pjaa.2023.v010i01.015","DOIUrl":"https://doi.org/10.46753/pjaa.2023.v010i01.015","url":null,"abstract":". In quantum mechanics, a Hilbert space administer a structure (linear) for physical states and also provide an inner product to convey physically-measurable expectation values. Keeping this aspect in mind, in this paper, we prove some significant properties concerning operator valued frames (OPV-frames). Also, we construct OPV-frames with the help of some given operators. Finally, we consider perturbation of OPV-frames and discuss the stability of OPV-frames.","PeriodicalId":37079,"journal":{"name":"Poincare Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43945052","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 : 2022-12-31DOI: 10.46753/pjaa.2022.v09i02.015
†. Jhavilalghimire, And Narayan, Prasad Pahari, Sumit Kumar
. Schauder frames satisfying property (I) and property (II) has been defined and studied. It has been proved that an atomic decomposition satisfies property (I) if and only if it satisfies property (II). Also, Schauder frames satisfying property ( M ) has been defined and it has been proved that, in a uniformly convex Banach space, if a Schauder frame satisfies property ( M ) , then it also satisfies property (II) (and hence property (I)). Further, we define atomic decompositions satisfying property ( B ) and prove that property ( B ) is a necessary condition for an atomic decomposition satisfying property (I). Finally, we define property ( SB ) for a Schauder frame and gave a necessary condition for it.
{"title":"CERTAIN PROPERTIES ASSOCIATED WITH SCHAUDER FRAMES IN BANACH SPACES","authors":"†. Jhavilalghimire, And Narayan, Prasad Pahari, Sumit Kumar","doi":"10.46753/pjaa.2022.v09i02.015","DOIUrl":"https://doi.org/10.46753/pjaa.2022.v09i02.015","url":null,"abstract":". Schauder frames satisfying property (I) and property (II) has been defined and studied. It has been proved that an atomic decomposition satisfies property (I) if and only if it satisfies property (II). Also, Schauder frames satisfying property ( M ) has been defined and it has been proved that, in a uniformly convex Banach space, if a Schauder frame satisfies property ( M ) , then it also satisfies property (II) (and hence property (I)). Further, we define atomic decompositions satisfying property ( B ) and prove that property ( B ) is a necessary condition for an atomic decomposition satisfying property (I). Finally, we define property ( SB ) for a Schauder frame and gave a necessary condition for it.","PeriodicalId":37079,"journal":{"name":"Poincare Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42686980","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 : 2022-12-31DOI: 10.46753/pjaa.2022.v09i02.004
{"title":"GENERATION OF FRACTALS AND ANTI-FRACTALS USING THAKUR ITERATIVE SCHEME","authors":"","doi":"10.46753/pjaa.2022.v09i02.004","DOIUrl":"https://doi.org/10.46753/pjaa.2022.v09i02.004","url":null,"abstract":"","PeriodicalId":37079,"journal":{"name":"Poincare Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47209787","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 : 2022-12-31DOI: 10.46753/pjaa.2022.v09i02.012
{"title":"SOME RESULTS ON DIFFERENTIAL-DIFFERENCE PAINLEVÉ EQUATIONS","authors":"","doi":"10.46753/pjaa.2022.v09i02.012","DOIUrl":"https://doi.org/10.46753/pjaa.2022.v09i02.012","url":null,"abstract":"","PeriodicalId":37079,"journal":{"name":"Poincare Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46119742","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}