Pub Date : 2021-11-15DOI: 10.30546/2409-4994.47.2.286
{"title":"Calderón-Zygmund operators with kernels of Dini's type and their multilinear commutators on generalized variable exponent Morrey spaces","authors":"","doi":"10.30546/2409-4994.47.2.286","DOIUrl":"https://doi.org/10.30546/2409-4994.47.2.286","url":null,"abstract":"","PeriodicalId":54068,"journal":{"name":"Proceedings of the Institute of Mathematics and Mechanics","volume":"27 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79315815","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 : 2021-11-15DOI: 10.30546/2409-4994.47.2.226
{"title":"ON THE ERROR OF APPROXIMATION BY RBF NEURAL NETWORKS WITH TWO HIDDEN NODES","authors":"","doi":"10.30546/2409-4994.47.2.226","DOIUrl":"https://doi.org/10.30546/2409-4994.47.2.226","url":null,"abstract":"","PeriodicalId":54068,"journal":{"name":"Proceedings of the Institute of Mathematics and Mechanics","volume":"21 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74744427","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 : 2021-11-15DOI: 10.30546/2409-4994.47.2.205
{"title":"CONVERSE THEOREM OF THE APPROXIMATION THEORY OF FUNCTIONS IN MORREY-SMIRNOV CLASSES RELATED TO THE DERIVATIVES OF FUNCTIONS","authors":"","doi":"10.30546/2409-4994.47.2.205","DOIUrl":"https://doi.org/10.30546/2409-4994.47.2.205","url":null,"abstract":"","PeriodicalId":54068,"journal":{"name":"Proceedings of the Institute of Mathematics and Mechanics","volume":"47 16","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72409332","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 : 2021-09-18DOI: 10.30546/2409-4994.48.2.2022.179
M. Garayev, H. Guediri, N. Altwaijry
For a bounded linear operator A on a reproducing kernel Hilbert space H (Ω), with normalized reproducing kernel b k λ = k λ k k λ k , the Berezin symbol, Berezin number and Berezin norm are defined respectively by e A ( λ ) = h A b k λ , b k λ i , ber ( A ) = sup λ ∈ Ω (cid:12)(cid:12)(cid:12) e A ( λ ) (cid:12)(cid:12)(cid:12) and k A k ber = sup λ ∈ Ω (cid:13)(cid:13)(cid:13) A b k λ (cid:13)(cid:13)(cid:13) . A straightforward comparison between these character-istics yields the inequalities ber ( A ) ≤ k A k ber ≤ k A k . In this paper, we prove further inequalities relating them, and give special care to the corresponding reverse inequalities. In particular, we refine the first one of the above inequalities, namely we prove that ber ( A ) ≤ (cid:18) k A k 2 ber − inf λ ∈ Ω (cid:13)(cid:13)(cid:13) ( A − e A ( λ )) b k λ (cid:13)(cid:13)(cid:13) 2 (cid:19) 12 .
为有界的线性算子在再生核希尔伯特空间H(Ω),与标准化复制内核b kλ= kλk kλk, Berezin符号,Berezin数量和Berezin规范定义分别通过e(λ)= H b kλ,我kλ,误码率(a) =一口λ∈Ω(cid: 12) (cid: 12) (cid: 12) e(λ)(cid: 12) (cid: 12) (cid: 12)和k = k误码率一口λ∈Ω(cid: 13) (cid: 13) (cid: 13) b kλ(cid: 13) (cid: 13) (cid: 13)。对这些特性的直接比较得出不等式ber (A)≤k A k ber≤k A k。本文进一步证明了与它们有关的不等式，并特别注意了相应的逆不等式。特别地，我们改进了上面的第一个不等式，即证明了ber (A)≤(cid:18) k A k 2 ber−inf λ∈Ω (cid:13)(cid:13)(cid:13) (cid:13))(A−e A (λ)) b k λ (cid:13)(cid:13)(cid:13) 2 (cid:19) 12。
{"title":"REVERSE INEQUALITIES FOR THE BEREZIN NUMBER OF\u0000OPERATORS","authors":"M. Garayev, H. Guediri, N. Altwaijry","doi":"10.30546/2409-4994.48.2.2022.179","DOIUrl":"https://doi.org/10.30546/2409-4994.48.2.2022.179","url":null,"abstract":"For a bounded linear operator A on a reproducing kernel Hilbert space H (Ω), with normalized reproducing kernel b k λ = k λ k k λ k , the Berezin symbol, Berezin number and Berezin norm are defined respectively by e A ( λ ) = h A b k λ , b k λ i , ber ( A ) = sup λ ∈ Ω (cid:12)(cid:12)(cid:12) e A ( λ ) (cid:12)(cid:12)(cid:12) and k A k ber = sup λ ∈ Ω (cid:13)(cid:13)(cid:13) A b k λ (cid:13)(cid:13)(cid:13) . A straightforward comparison between these character-istics yields the inequalities ber ( A ) ≤ k A k ber ≤ k A k . In this paper, we prove further inequalities relating them, and give special care to the corresponding reverse inequalities. In particular, we refine the first one of the above inequalities, namely we prove that ber ( A ) ≤ (cid:18) k A k 2 ber − inf λ ∈ Ω (cid:13)(cid:13)(cid:13) ( A − e A ( λ )) b k λ (cid:13)(cid:13)(cid:13) 2 (cid:19) 12 .","PeriodicalId":54068,"journal":{"name":"Proceedings of the Institute of Mathematics and Mechanics","volume":"32 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87937886","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 : 2021-06-20DOI: 10.30546/2409-4994.47.1.197
{"title":"HIDAYAT MAHAMMAD OGLU HUSEYNOV–70","authors":"","doi":"10.30546/2409-4994.47.1.197","DOIUrl":"https://doi.org/10.30546/2409-4994.47.1.197","url":null,"abstract":"","PeriodicalId":54068,"journal":{"name":"Proceedings of the Institute of Mathematics and Mechanics","volume":"33 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72946981","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 : 2021-06-20DOI: 10.30546/2409-4994.47.1.46
Ulkar Gurbanova
{"title":"Bifurcation in nonlinear Sturm-Liouville problems with indefinite weight and spectral parameter in the boundary condition","authors":"Ulkar Gurbanova","doi":"10.30546/2409-4994.47.1.46","DOIUrl":"https://doi.org/10.30546/2409-4994.47.1.46","url":null,"abstract":"","PeriodicalId":54068,"journal":{"name":"Proceedings of the Institute of Mathematics and Mechanics","volume":"25 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84007591","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 : 2021-06-20DOI: 10.30546/2409-4994.47.1.112
T. Yuldashev, B. J. Kadirkulov
In this paper, we consider a boundary value problem for a mixed type partial differential equation with Hilfer operator of fractional integro-differentiation in a positive rectangular domain and with spectral parameter in a negative rectangular domain. The mixed differential equation depends from another positive small parameter in mixed derivatives. The considering mixed type differential equation brings to a spectral problem for a second order differential equation with respect to the second variable. Regarding the first variable, this equation is an ordinary fractional differential equation in the positive part of the considering segment, and is a second-order ordinary differential equation with spectral parameter in the negative part of this segment. Using the spectral method of separation of variables, the solution of the boundary value problem is constructed in the form of a Fourier series. Theorems on the existence and uniqueness of the problem are proved for regular values of the spectral parameter. It is proved the stability of solution with respect to boundary function and with respect to small positive parameter given in mixed derivatives. For irregular values of the spectral parameter, an infinite number of solutions in the form of a Fourier series are constructed. 1. Problem statement In a rectangular domain Ω = {(t, x) : −a < t < b, 0 < x < l} we consider the fractional partial differential equation of mixed type 0 = ( D α, γ − ν D α, γ ∂2 ∂ x2 − ∂2 ∂ x2 ) U (t, x), (t, x) ∈ Ω 1, ( ∂ 2 ∂ t 2 − ν ∂ 4 ∂ t 2 ∂ x 2 − ω2 ∂ 2 ∂ x 2 ) U (t, x), (t, x) ∈ Ω 2, (1.1) where Ω 1 = {(t, x) : 0 < t < b, 0 < x < l}, Ω 2 = {(t, x) : −a < t < 0, 0 < x < l}, ν is positive parameter, ω is positive spectral parameter, a, b are positive real numbers, D γ = Jγ−α 0+ d dt J1−γ 0+ , 0 < α ≤ γ ≤ 1 2010 Mathematics Subject Classification. 35M12, 35J25, 35L20, 30E20, 45E05.
本文研究了正矩形域上具有分数阶积分微分的Hilfer算子和负矩形域上具有谱参数的混合型偏微分方程的边值问题。混合微分方程依赖于混合导数中的另一个正小参数。考虑的混合型微分方程涉及到二阶微分方程关于二阶变量的谱问题。对于第一个变量，该方程在考虑段的正部分为普通分数阶微分方程，在考虑段的负部分为带谱参数的二阶常微分方程。利用分离变量的谱方法，将边值问题的解构造为傅里叶级数形式。对于谱参数的正则值，证明了问题的存在唯一性定理。证明了混合导数中解对边界函数和对小正参数的稳定性。对于谱参数的不规则值，以傅里叶级数的形式构造了无穷多个解。1. 问题陈述在矩形域Ω= {(t, x):−< t < b, 0 < x < l}我们考虑部分混合型偏微分方程0 =(Dα、γ−νDα、γ∂2∂x2−∂2∂x2) U (t, x), (t, x)∈Ω1(∂2∂t 2−ν∂4∂t 2∂x 2−ω2∂2∂x 2) U (t, x), (t, x)∈Ω2(1.1),Ω1 = {(t, x): 0 < t < b, 0 < x < l},Ω2 = {(t, x):−a < t < 0,0 < x < l}， ν为正参数，ω为正谱参数，a, b为正实数，D γ = Jγ−α 0+ D dt J1−γ 0+， 0 < α≤γ≤1 2010数学学科分类。35M12, 35J25, 35L20, 30E20, 45E05。
{"title":"On a boundary value problem for a mixed type fractional differential equations with parameters","authors":"T. Yuldashev, B. J. Kadirkulov","doi":"10.30546/2409-4994.47.1.112","DOIUrl":"https://doi.org/10.30546/2409-4994.47.1.112","url":null,"abstract":"In this paper, we consider a boundary value problem for a mixed type partial differential equation with Hilfer operator of fractional integro-differentiation in a positive rectangular domain and with spectral parameter in a negative rectangular domain. The mixed differential equation depends from another positive small parameter in mixed derivatives. The considering mixed type differential equation brings to a spectral problem for a second order differential equation with respect to the second variable. Regarding the first variable, this equation is an ordinary fractional differential equation in the positive part of the considering segment, and is a second-order ordinary differential equation with spectral parameter in the negative part of this segment. Using the spectral method of separation of variables, the solution of the boundary value problem is constructed in the form of a Fourier series. Theorems on the existence and uniqueness of the problem are proved for regular values of the spectral parameter. It is proved the stability of solution with respect to boundary function and with respect to small positive parameter given in mixed derivatives. For irregular values of the spectral parameter, an infinite number of solutions in the form of a Fourier series are constructed. 1. Problem statement In a rectangular domain Ω = {(t, x) : −a < t < b, 0 < x < l} we consider the fractional partial differential equation of mixed type 0 = ( D α, γ − ν D α, γ ∂2 ∂ x2 − ∂2 ∂ x2 ) U (t, x), (t, x) ∈ Ω 1, ( ∂ 2 ∂ t 2 − ν ∂ 4 ∂ t 2 ∂ x 2 − ω2 ∂ 2 ∂ x 2 ) U (t, x), (t, x) ∈ Ω 2, (1.1) where Ω 1 = {(t, x) : 0 < t < b, 0 < x < l}, Ω 2 = {(t, x) : −a < t < 0, 0 < x < l}, ν is positive parameter, ω is positive spectral parameter, a, b are positive real numbers, D γ = Jγ−α 0+ d dt J1−γ 0+ , 0 < α ≤ γ ≤ 1 2010 Mathematics Subject Classification. 35M12, 35J25, 35L20, 30E20, 45E05.","PeriodicalId":54068,"journal":{"name":"Proceedings of the Institute of Mathematics and Mechanics","volume":"53 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75710822","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 : 2021-06-20DOI: 10.30546/2409-4994.47.1.3
J. Jonnalagadda, D. Baleanu
{"title":"Solutions for a Nabla Fractional Boundary Value Problem with Discrete Mittag--Leffler Kernel","authors":"J. Jonnalagadda, D. Baleanu","doi":"10.30546/2409-4994.47.1.3","DOIUrl":"https://doi.org/10.30546/2409-4994.47.1.3","url":null,"abstract":"","PeriodicalId":54068,"journal":{"name":"Proceedings of the Institute of Mathematics and Mechanics","volume":"5 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87610312","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 : 2021-06-20DOI: 10.30546/2409-4994.47.1.55
D. Israfilov, Elife Gursel
{"title":"Direct and Inverse Theorems in Variable Exponent Smirnov Classes","authors":"D. Israfilov, Elife Gursel","doi":"10.30546/2409-4994.47.1.55","DOIUrl":"https://doi.org/10.30546/2409-4994.47.1.55","url":null,"abstract":"","PeriodicalId":54068,"journal":{"name":"Proceedings of the Institute of Mathematics and Mechanics","volume":"49 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83108001","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 : 2021-06-20DOI: 10.30546/2409-4994.47.1.138
A. Khanmamedov, A. F. Mamedova
{"title":"A note on the Schrodinger operator with exponential potential","authors":"A. Khanmamedov, A. F. Mamedova","doi":"10.30546/2409-4994.47.1.138","DOIUrl":"https://doi.org/10.30546/2409-4994.47.1.138","url":null,"abstract":"","PeriodicalId":54068,"journal":{"name":"Proceedings of the Institute of Mathematics and Mechanics","volume":"68 2 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89388063","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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