Abstract In this work, we are concerned with a generalized Steklov problem with (p(x), q(x))-Laplacian operator. Under some appropriate conditions on the data involved in the elliptic problem, we prove the existence of at least three solutions using Ricceri’s three critical points theorem.
{"title":"Existence and multiplicity results for a Steklov problem involving (p(x), q(x))-Laplacian operator","authors":"B. Karim, A. Lakhdi, M. Ammi, A. Zerouali","doi":"10.2478/mjpaa-2022-0004","DOIUrl":"https://doi.org/10.2478/mjpaa-2022-0004","url":null,"abstract":"Abstract In this work, we are concerned with a generalized Steklov problem with (p(x), q(x))-Laplacian operator. Under some appropriate conditions on the data involved in the elliptic problem, we prove the existence of at least three solutions using Ricceri’s three critical points theorem.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49536922","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}
Abstract We introduce and investigate the injective hull of the strongly Lipschitz classical p-compact operator ideal defined between a pointed metric space and a Banach space. As an application we extend some characterizations of the injective hull of the strongly Lipschitz classical p-compact from the linear case to the Lipschitz case. Also, we introduce the ideal of Lipschitz unconditionally quasi p-nuclear operators between pointed metric spaces and show that it coincides with the Lipschitz injective hull of the ideal of Lipschitz classical p-compact operators.
{"title":"The ideal of Lipschitz classical p-compact operators and its injective hull","authors":"T. Tiaiba, D. Achour","doi":"10.2478/mjpaa-2022-0003","DOIUrl":"https://doi.org/10.2478/mjpaa-2022-0003","url":null,"abstract":"Abstract We introduce and investigate the injective hull of the strongly Lipschitz classical p-compact operator ideal defined between a pointed metric space and a Banach space. As an application we extend some characterizations of the injective hull of the strongly Lipschitz classical p-compact from the linear case to the Lipschitz case. Also, we introduce the ideal of Lipschitz unconditionally quasi p-nuclear operators between pointed metric spaces and show that it coincides with the Lipschitz injective hull of the ideal of Lipschitz classical p-compact operators.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44034173","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}
Abstract In this paper, we valorize the relationship between positive p−summing operators and positive strongly q−summing operators using (Contemp. Math. 328, 145 − 149 (2003)).
{"title":"Bu’s theorem in the positive situation","authors":"A. Bougoutaia, A. Belacel","doi":"10.2478/mjpaa-2022-0002","DOIUrl":"https://doi.org/10.2478/mjpaa-2022-0002","url":null,"abstract":"Abstract In this paper, we valorize the relationship between positive p−summing operators and positive strongly q−summing operators using (Contemp. Math. 328, 145 − 149 (2003)).","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45157476","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}
Abstract In [Appl. Comput. Harmon. Anal., 46 (2019), 664673] O. Christensen and M. Hasannasab observed that assuming the existence of an operator T sending en to en+1 for all n ∈ ℕ (where (en)n∈ℕ is a sequence of vectors) guarantees that (en)n∈ℕ is linearly independent if and only if dim{en}n∈ℕ = ∞. In this article, we recover this result as a particular case of a general order-theory-based model-theoretic result. We then return to the context of vector spaces to show that, if we want to use a condition like T(ei) = eϕ(i) for all i ∈ I where I is countable as a replacement of the previous one, the conclusion will only stay true if ϕ : I → I is conjugate to the successor function succ : n ↦n + 1 defined on ℕ. We finally prove a tentative generalization of the result, where we replace the condition T(ei) = eϕ(i) for all i ∈ I where ϕ is conjugate to the successor function with a more sophisticated one, and to which we have not managed to find a new application yet.
{"title":"Independence, infinite dimension, and operators","authors":"Nizar El Idrissi, S. Kabbaj","doi":"10.2478/mjpaa-2023-0006","DOIUrl":"https://doi.org/10.2478/mjpaa-2023-0006","url":null,"abstract":"Abstract In [Appl. Comput. Harmon. Anal., 46 (2019), 664673] O. Christensen and M. Hasannasab observed that assuming the existence of an operator T sending en to en+1 for all n ∈ ℕ (where (en)n∈ℕ is a sequence of vectors) guarantees that (en)n∈ℕ is linearly independent if and only if dim{en}n∈ℕ = ∞. In this article, we recover this result as a particular case of a general order-theory-based model-theoretic result. We then return to the context of vector spaces to show that, if we want to use a condition like T(ei) = eϕ(i) for all i ∈ I where I is countable as a replacement of the previous one, the conclusion will only stay true if ϕ : I → I is conjugate to the successor function succ : n ↦n + 1 defined on ℕ. We finally prove a tentative generalization of the result, where we replace the condition T(ei) = eϕ(i) for all i ∈ I where ϕ is conjugate to the successor function with a more sophisticated one, and to which we have not managed to find a new application yet.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46731814","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}
Abstract In this paper, we investigate several interesting properties for certain class of analytic functions defined by q-analogue of p-valent Cătaş operator. All our results are sharp.
{"title":"Certain Classes of Analytic Functions Associated With q-Analogue of p-Valent Cătaş Operator","authors":"M. Aouf, S. Madian","doi":"10.2478/mjpaa-2021-0029","DOIUrl":"https://doi.org/10.2478/mjpaa-2021-0029","url":null,"abstract":"Abstract In this paper, we investigate several interesting properties for certain class of analytic functions defined by q-analogue of p-valent Cătaş operator. All our results are sharp.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45165479","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}
Abstract In the present paper a generalization of the Laplace transform is introduced and studied. Its inversion formula is also obtained. As an application, we obtain the generalized fractional Laplace transform of a general class of functions and a product of the Fox’s H- function and general class of functions. The results obtained are of general nature and capable of yielding a large number of known or new results as special cases. For illustration, some special cases involving important special functions are mentioned.
{"title":"On the generalized fractional Laplace transform","authors":"Virendra Kumar","doi":"10.2478/mjpaa-2021-0030","DOIUrl":"https://doi.org/10.2478/mjpaa-2021-0030","url":null,"abstract":"Abstract In the present paper a generalization of the Laplace transform is introduced and studied. Its inversion formula is also obtained. As an application, we obtain the generalized fractional Laplace transform of a general class of functions and a product of the Fox’s H- function and general class of functions. The results obtained are of general nature and capable of yielding a large number of known or new results as special cases. For illustration, some special cases involving important special functions are mentioned.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46319055","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}
Abstract The aim of this paper is to work out the solvability of a class of Caputo time fractional problems with boundary integral conditions. A generalized formula of integration is demonstrated and applied to establish the a priori estimate of the solution, then we prove the existence which is based on the range density of the operator associated with the problem.
{"title":"On a Class of Caputo Time Fractional Problems with Boundary Integral Conditions","authors":"Karim Aggoun, A. Merad","doi":"10.2478/mjpaa-2021-0027","DOIUrl":"https://doi.org/10.2478/mjpaa-2021-0027","url":null,"abstract":"Abstract The aim of this paper is to work out the solvability of a class of Caputo time fractional problems with boundary integral conditions. A generalized formula of integration is demonstrated and applied to establish the a priori estimate of the solution, then we prove the existence which is based on the range density of the operator associated with the problem.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46444759","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}
Abstract In the present paper, we study the Jacobson’s Lemma in the unital ring of all bounded right linear operators ℬR(X) acting on a two-sided quaternionic Banach space X. In particular, let A, B ∈ ℬR(X) and let q ∈ ℍ {0}, we prove that w(AB) {0} = w(BA) {0} where w belongs to the spherical spectrum, the spherical approximate point spectrum, the right spherical spectrum, the left spherical spectrum, the spherical point spectrum, the spherical residual spectrum and the spherical continuous spectrum. We also prove that the range of (AB)2 − 2Re(q)AB + |q|2I is closed if and only if (BA)2 − 2Re(q)BA + |q|2I has closed range. Finally, we show that (AB)2 − 2Re(q)AB + |q|2I is Drazin invertible if and only if (BA)2 − 2Re(q)BA + |q|2I is.
{"title":"Jacobson’s Lemma in the ring of quaternionic linear operators","authors":"E. Benabdi, M. Barraa","doi":"10.2478/mjpaa-2021-0031","DOIUrl":"https://doi.org/10.2478/mjpaa-2021-0031","url":null,"abstract":"Abstract In the present paper, we study the Jacobson’s Lemma in the unital ring of all bounded right linear operators ℬR(X) acting on a two-sided quaternionic Banach space X. In particular, let A, B ∈ ℬR(X) and let q ∈ ℍ {0}, we prove that w(AB) {0} = w(BA) {0} where w belongs to the spherical spectrum, the spherical approximate point spectrum, the right spherical spectrum, the left spherical spectrum, the spherical point spectrum, the spherical residual spectrum and the spherical continuous spectrum. We also prove that the range of (AB)2 − 2Re(q)AB + |q|2I is closed if and only if (BA)2 − 2Re(q)BA + |q|2I has closed range. Finally, we show that (AB)2 − 2Re(q)AB + |q|2I is Drazin invertible if and only if (BA)2 − 2Re(q)BA + |q|2I is.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43653181","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}
Abstract In this paper, an efficient algorithm is proposed for solving one dimensional time-space-fractional telegraph equations. The fractional derivatives are described in the conformable sense. This algorithm is based on shifted Chebyshev polynomials of the fourth kind. The time-space fractional telegraph equations is reduced to a linear system of second order differential equations and the Newmark’s method is applied to solve this system. Finally, some numerical examples are presented to confirm the reliability and effectiveness of this algorithm.
{"title":"An efficient algorithm for solving the conformable time-space fractional telegraph equations","authors":"Abdelkebir Saad, N. Brahim","doi":"10.2478/mjpaa-2021-0028","DOIUrl":"https://doi.org/10.2478/mjpaa-2021-0028","url":null,"abstract":"Abstract In this paper, an efficient algorithm is proposed for solving one dimensional time-space-fractional telegraph equations. The fractional derivatives are described in the conformable sense. This algorithm is based on shifted Chebyshev polynomials of the fourth kind. The time-space fractional telegraph equations is reduced to a linear system of second order differential equations and the Newmark’s method is applied to solve this system. Finally, some numerical examples are presented to confirm the reliability and effectiveness of this algorithm.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47740942","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}
Abstract In this note, we study the Radon transform and its dual on the discrete matrices by defining hyperplanes as being infinite sets of solutions of linear Diophantine equations. We then give an inversion formula and a support theorem.
{"title":"Integral geometry on discrete matrices","authors":"Abdelbaki Attioui","doi":"10.2478/mjpaa-2021-0024","DOIUrl":"https://doi.org/10.2478/mjpaa-2021-0024","url":null,"abstract":"Abstract In this note, we study the Radon transform and its dual on the discrete matrices by defining hyperplanes as being infinite sets of solutions of linear Diophantine equations. We then give an inversion formula and a support theorem.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48901990","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：