Methods of Functional Analysis and Topology最新文献

{"title":"Stability of dual $g$-fusion frames in Hilbert spaces","authors":"Prasenjit Ghosh, T. Samanta","doi":"10.31392/MFAT-npu26_3.2020.04","DOIUrl":"https://doi.org/10.31392/MFAT-npu26_3.2020.04","url":null,"abstract":"We give a characterization of K-g-fusion frames and discuss the stability of dual g-fusion frames. We also present a necessary and su cient condition for a quotient operator to be bounded.  ¤ õâìáï å à aâ¥à÷§ æ÷ï K-g ä३¬÷¢ §« ̈ââï â ஧£«ï¤ õâìáï áâ÷©a ̈áâì ¤¢®ùáâ ̈å g-ä ̄¥©¬÷¢ §« ̈ââï. ’ a®¦ ­ ¤ îâìáï ­¥®¡å÷¤­÷ â ¤®áâ â­÷ 㬮¢ ̈ ®¡¬¥¦¥­­®áâ÷ ® ̄¥à â®à ä aâ®à ̈§ æ÷ù.","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"26 1","pages":"227-240"},"PeriodicalIF":0.4,"publicationDate":"2020-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48394408","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":"Unique solvability of a Dirichlet problem for a fractional parabolic equation using energy-inequality method","authors":"Benaoua Antara, Oussaeif Taki-Eddine, Rezzoug Imad","doi":"10.31392/mfat-npu26_3.2020.03","DOIUrl":"https://doi.org/10.31392/mfat-npu26_3.2020.03","url":null,"abstract":"In this paper, we establish su cient conditions for the existence and uniqueness of the solution in fractional functional space for a class of initial boundaryvalue problems for a class of partial fractional parabolic di erential equations that include a fractional derivative of Caputo. The results are established by the application of the method based on a priori estimate \"energy inequality\" and the density of the range of the operator generated by the problem considered. ‚áâ ­®¢«¥­÷ ¤®áâ â­÷ 㬮¢ ̈ ÷á­ã¢ ­­ï â õ¤ ̈­®áâ÷ ஧¢'ï§aã § ¤à®¡®¢®£® äã­aæ÷®­ «ì­®£® ̄à®áâ®àã ¤«ï ®¤­®£® a« áã ̄®ç âa®¢®-aà ©®¢ ̈å § ¤ ç ¤«ï ¤¥ïa ̈å ¤à®¡®¢®̄ à ¡®«÷ç­ ̈å ¤ ̈ä¥à¥­æ÷ «ì­ ̈å à÷¢­ï­ì ÷§ ¤à®¡®¢®î ̄®å÷¤­®î Š ̄ãâ®. ¥§ã«ìâ â ̈ ®âà ̈¬ ­® è«ï宬 § áâ®á㢠­­ï ¬¥â®¤ã ¥­¥à£¥â ̈ç­ ̈å ­¥à÷¢­®á⥩. „®¢¥¤¥­ é÷«ì­÷áâì ®¡à §ã ® ̄¥à â®à , é® ¢÷¤ ̄®¢÷¤ õ § ¤ ç÷.","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"26 1","pages":"216-226"},"PeriodicalIF":0.4,"publicationDate":"2020-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43726984","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":"Cantor's intersection theorem and some generalized fixed point theorems over a locally convex topological vector space","authors":"A. Baisnab, K. Roy, M. Saha","doi":"10.31392/mfat-npu26_3.2020.07","DOIUrl":"https://doi.org/10.31392/mfat-npu26_3.2020.07","url":null,"abstract":"","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"26 1","pages":"262-271"},"PeriodicalIF":0.4,"publicationDate":"2020-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48557919","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":"Viability result for higher-order functional \u0000differential inclusions","authors":"M. Aitalioubrahim","doi":"10.31392/mfat-npu26_3.2020.01","DOIUrl":"https://doi.org/10.31392/mfat-npu26_3.2020.01","url":null,"abstract":"We prove, in separable Banach spaces, the existence of viable solutions for the following higher-order functional di erential inclusion x(t) in F (t, T (t)x, x(t), ..., x(k 1)(t)), a.e. on [0, tau ]. We consider the case when the right-hand side is nonconvex and the constraint is moving. „®¢®¤ ̈âìáï ÷á­ã¢ ­­ï ¢ ᥠ̄ à ¡¥«ì­ ̈å ¡ ­ 客 ̈å ̄à®áâ®à å ஧¢'ï§a÷¢ ­ ¢á쮬ã ÷­â¥à¢ «÷ ¤«ï äã­aæ÷®­ «ì­®-¤ ̈ä¥à¥­æ÷ «ì­ ̈å ¢a«î祭ì x(t) in F (t, T (t)x, x(t), ..., x(k 1)(t)), a.e. on [0, tau ]. ®§£«ï¤ õâìáï ¢ ̈ ̄ ¤®a ­¥® ̄ãa«®ù ̄à ¢®ù ç áâ ̈­ ̈ â àã宬®£® ®¡¬¥¦¥­­ï.","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"26 1","pages":"189-200"},"PeriodicalIF":0.4,"publicationDate":"2020-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41690278","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":"Weak \u0000 solution for fractional $p(x)$-Laplacian problem with Dirichlet-type \u0000 boundary condition","authors":"Abdelali Sabri, A. Jamea, H. Alaoui","doi":"10.31392/mfat-npu26_3.2020.08","DOIUrl":"https://doi.org/10.31392/mfat-npu26_3.2020.08","url":null,"abstract":"In the present paper, we prove the existence and uniqueness result of weak solutions to a class of fractional p(x)-Laplacian problem with Dirichlet-type boundary condition, the main tool used here is the varitional method combined with the theory of fractional Sobolev spaces with variable exponent. „«ï ®¤­®£® a« áã § ¤ ç ÷§ ¤à®¡®¢ ̈¬ p(x)-« ̄« á÷ ­®¬ § £à ­ ̈ç­®î 㬮¢®î â ̈ ̄㠄 ̈à ̈å«¥ ¤®¢¥¤¥­® ⥮६ã ̄à® ÷á­ã¢ ­­ï â õ¤ ̈­÷áâì á« ¡a®£® ஧¢'ï§aã. ‚ ̈a®à ̈á⮢ãîâìáï ¢ à÷ æ÷©­ ̈© ¬¥â®¤ ÷ ⥮à÷ï ¤à®¡®¢ ̈å ̄à®áâ®à÷¢ ‘®¡®«¥¢ §¬÷­­®£® ̄®àï¤aã.","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"26 1","pages":"272-282"},"PeriodicalIF":0.4,"publicationDate":"2020-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44677935","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":"Norm inequalities for accretive-dissipative block matrices","authors":"Fadi Alrimawi, M. Al-khlyleh, F. A. Abushaheen","doi":"10.31392/mfat-npu26_3.2020.02","DOIUrl":"https://doi.org/10.31392/mfat-npu26_3.2020.02","url":null,"abstract":"Let T = [Tij ] in BbbM mn(BbbC ) be accretive-dissipative, where Tij in BbbM n(BbbC ) for i, j = 1, 2, ...,m. Let f be a function that is convex and increasing on [0,infty ) where f(0) = 0. Then bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| f left( sum i<j | Tij | right) + f left( sum i<j bigm| bigm| T ast jibigm| bigm| 2 right) bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| leq bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| f biggl( m2 m 2 | T | biggr) bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| . Also, if f is concave and increasing on [0,infty ) where f(0) = 0, then bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| f left( sum i<j | Tij | right) + f left( sum i<j bigm| bigm| T ast jibigm| bigm| 2 right) bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| leq (2m2 2m) bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| f Biggl( | T | 4 bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| . ¥å © T = Tij in BbbM mn(BbbC ), ¤¥ Tij in BbbM n(BbbC ) ̄à ̈ i, j = 1, 2, ...,m., { aà¥â ̈¢­®¤ ̈á ̈ ̄ â ̈¢­ ¬ âà ̈æï. ¥å © f ® ̄ãa« äã­aæ÷ï, ïa §à®áâ õ ­ [0,infty ), ¤¥ f(0) = 0. ’®¤÷ bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| f left( sum i<j | Tij | right) + f left( sum i<j bigm| bigm| T ast jibigm| bigm| 2 right) bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| leq bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| f biggl( m2 m 2 | T | biggr) bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| . ’ a®¦, ïaé® f õ 㣭ãâ®î, §à®áâ õ ­ [0,infty ) ÷ f(0) = 0, â® bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| f left( sum i<j | Tij | right) + f left( sum i<j bigm| bigm| T ast jibigm| bigm| 2 right) bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| leq (2m2 2m) bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| f Biggl( | T | 4 bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| bigm| .","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"9 5","pages":"201-215"},"PeriodicalIF":0.4,"publicationDate":"2020-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41298327","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":"Nonlocal eigenvalue problems with indefinite weight","authors":"S. Taarabti","doi":"10.31392/mfat-npu26_3.2020.09","DOIUrl":"https://doi.org/10.31392/mfat-npu26_3.2020.09","url":null,"abstract":"In the present paper, we consider a class of eigenvalue problems driven by a nonlocal integro-di erential operator scrL K with Dirichlet boundary conditions. Under certain assumptions on p and q, we establish that any lambda > 0 su ciently small is an eigenvalue of the nonhomogeneous nonlocal problem (scrP lambda ). ®§£«ï¤ õâìáï a« á á ̄¥aâà «ì­ ̈å § ¤ ç, ̄®¢'ï§ ­ ̈å ÷§ ­¥«®a «ì­ ̈¬ ÷­â¥£à®¤ ̈ä¥à¥­æ÷ «ì­ ̈¬ ® ̄¥à â®à®¬ scrL K ÷§ aà ©®¢®î 㬮¢®î „ ̈à ̈å«¥. ‡ ̄¥¢­ ̈å ̄à ̈ ̄ã饭ì 鮤® p ÷ q ¤®¢¥¤¥­®, é® a®¦­¥ ¤®áâ ­ì® ¬ «¥ lambda > 0 õ ¢« á­ ̈¬ §­ 祭­ï¬ ­¥®¤­®à÷¤­®ù ­¥«®a «ì­®ù § ¤ ç÷ (scrP lambda ).","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"26 1","pages":"283-294"},"PeriodicalIF":0.4,"publicationDate":"2020-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49295825","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":"Green Measures for Time Changed Markov Processes","authors":"J. L. D. Silva, Y. Kondratiev","doi":"10.31392/mfat-npu26_3.2021.04","DOIUrl":"https://doi.org/10.31392/mfat-npu26_3.2021.04","url":null,"abstract":"In this paper we study Green measures for certain classes of random time change Markov processes where the random time change are inverse subordinators. We show the existence of the Green measure for these processes under the condition of the existence of the Green measure of the original Markov processes and they coincide. Applications to fractional dynamics in given.","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47316037","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 analogue of the logarithmic $(u,v)$-derivative and its application","authors":"R. Osaulenko","doi":"10.31392/mfat-npu26_2.2020.09","DOIUrl":"https://doi.org/10.31392/mfat-npu26_2.2020.09","url":null,"abstract":"We study an analogue of the logarithmic (u, v)-derivative. The last one has many interesting properties and good ways to calculate it. To show how it can be used we apply it to a model class of nowhere monotone functions that are composition of Salem function and nowhere differentiable functions.","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"26 1","pages":"179-188"},"PeriodicalIF":0.4,"publicationDate":"2020-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44027986","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 a new class of operators related to quasi-Fredholm operators","authors":"Z. Garbouj, H. Skhiri","doi":"10.31392/mfat-npu26_2.2020.06","DOIUrl":"https://doi.org/10.31392/mfat-npu26_2.2020.06","url":null,"abstract":"In this paper, we introduce a generalization of quasi-Fredholm operators [7] to k-quasi-Fredholm operators on Hilbert spaces for nonnegative integer k. The case when k = 0, represents the set of quasi-Fredholm operators and the meeting of the classes of k-quasi-Fredholm operators is called the class of pseudoquasi-Fredholm operators. We present some fundamental properties of the operators belonging to these classes and, as applications, we prove some spectral theorem and finite-dimensional perturbations results for these classes. Also, the notion of new index of a pseudo-quasi-Fredholm operator called pq-index is introduced and the stability of this index by finite-dimensional perturbations is proved. This paper extends some results proved in [5] to closed unbounded operators.","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"26 1","pages":"141-166"},"PeriodicalIF":0.4,"publicationDate":"2020-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47404836","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}