This present work aims to ameliorate the celebrated Cauchy-Schwarz inequality and provide several new consequences associated with the numerical radius upper bounds of Hilbert space operators. More precisely, for arbitrary a, b ? H and ? ? 0, we show that |?a,b?|2 ? 1 ? + 1 ?a??b?|?a, b?| + ?/?+1 ?a?2?b?2 ? ?a?2?b?2. As a consequence, we provide several new upper bounds for the numerical radius that refine and generalize some of Kittaneh?s results in [A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix. Studia Math. 2003;158:11-17] and [Cauchy-Schwarz type inequalities and applications to numerical radius inequalities. Math. Inequal. Appl. 2020;23:1117-1125], respectively. In particular, for arbitrary A, B ? B(H) and ? ? 0, we show the following sharp upper bound w2 (B*A) ? 1/2?+2 ?|A|2 + B|2?w(B*A)+ ?/2?+2 ?|A|4 + |B?4, with equality holds when A=B= (0100). It is also worth mentioning here that some specific values of ? ? 0 provide more accurate estimates for the numerical radius. Finally, some related upper bounds are also provided.
本文旨在改进著名的Cauchy-Schwarz不等式，并提供与Hilbert空间算子数值半径上界相关的几个新结果。更准确地说，对于任意的a b ?H和?？ 0，我们显示|?a,b?| 2 ?1 ？ + 1 ?a? b? b| ?a、b吗?| + /?2 + 1 ? ? ? ?2呢?一个2 ? b ? 2。因此，我们提供了几个新的数值半径上界，这些上界改进和推广了Kittaneh?得到了一个数值半径不等式和Frobenius伴矩阵的数值半径估计。[j] .数学学报，2003;58(1):11-17。数学。不平等的。[app . 2020;23:1117-1125]。特别是对于任意的A B ?B(H)和?？ 0，我们给出下面的明显上界w2 (B*A) ?半吗?+2 ?|A|2 + B|2?w(B*A)+ ?/2?+2 ?| a |4 + | b ?4、当A=B=(0100)时等式成立。这里还值得一提的是?？ 0为数值半径提供了更准确的估计。最后给出了相关的上界。
{"title":"A refinement of the Cauchy-Schwarz inequality accompanied by new numerical radius upper bounds","authors":"Mohammed Al-Dolat, Imad Jaradat","doi":"10.2298/fil2303971a","DOIUrl":"https://doi.org/10.2298/fil2303971a","url":null,"abstract":"This present work aims to ameliorate the celebrated Cauchy-Schwarz inequality and provide several new consequences associated with the numerical radius upper bounds of Hilbert space operators. More precisely, for arbitrary a, b ? H and ? ? 0, we show that |?a,b?|2 ? 1 ? + 1 ?a??b?|?a, b?| + ?/?+1 ?a?2?b?2 ? ?a?2?b?2. As a consequence, we provide several new upper bounds for the numerical radius that refine and generalize some of Kittaneh?s results in [A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix. Studia Math. 2003;158:11-17] and [Cauchy-Schwarz type inequalities and applications to numerical radius inequalities. Math. Inequal. Appl. 2020;23:1117-1125], respectively. In particular, for arbitrary A, B ? B(H) and ? ? 0, we show the following sharp upper bound w2 (B*A) ? 1/2?+2 ?|A|2 + B|2?w(B*A)+ ?/2?+2 ?|A|4 + |B?4, with equality holds when A=B= (0100). It is also worth mentioning here that some specific values of ? ? 0 provide more accurate estimates for the numerical radius. Finally, some related upper bounds are also provided.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68268515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study the existence and uniqueness of solutions for a multiple system of fractional differential equations with nonlocal integro multi point boundary conditions by using the p-Laplacian operator and the ?-Caputo derivatives. The presented results are obtained by the two fixed point theorems of Banach and Krasnoselskii. An illustrative example is presented at the end to show the applicability of the obtained results. To the best of our knowledge, this is the first time where such problem is considered.
{"title":"An existence study for a multiple system with p−Laplacian involving φ−Caputo derivatives","authors":"Hamid Beddani, M. Beddani, Z. Dahmani","doi":"10.2298/fil2306879b","DOIUrl":"https://doi.org/10.2298/fil2306879b","url":null,"abstract":"In this paper, we study the existence and uniqueness of solutions for a multiple system of fractional differential equations with nonlocal integro multi point boundary conditions by using the p-Laplacian operator and the ?-Caputo derivatives. The presented results are obtained by the two fixed point theorems of Banach and Krasnoselskii. An illustrative example is presented at the end to show the applicability of the obtained results. To the best of our knowledge, this is the first time where such problem is considered.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68271619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This research investigates k-Almost Newton-Ricci solitons (k-ANRS) embedded in a metallic Riemannian manifold Mn having the potential function ?. Furthermore, we prove geodesic and minimal conditions for hypersurfaces of metallic Riemannian manifolds. Beside this, we have explained some applications of metallic Riemannian manifold admitting k-Almost Newton-Ricci solitons.
{"title":"Hypersurfaces of metallic Riemannian manifolds as k-Almost Newton-Ricci solitons","authors":"Ali Choudhary, M. Siddiqi, O. Bahadır, S. Uddin","doi":"10.2298/fil2307187c","DOIUrl":"https://doi.org/10.2298/fil2307187c","url":null,"abstract":"This research investigates k-Almost Newton-Ricci solitons (k-ANRS) embedded in a metallic Riemannian manifold Mn having the potential function ?. Furthermore, we prove geodesic and minimal conditions for hypersurfaces of metallic Riemannian manifolds. Beside this, we have explained some applications of metallic Riemannian manifold admitting k-Almost Newton-Ricci solitons.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68272604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work deals with a new generalization of r-Stirling numbers using l-tuple of permutations and partitions called (l,r)-Stirling numbers of both kinds. We study various properties of these numbers using combinatorial interpretations and symmetric functions. Also, we give a limit representation of the multiple zeta function using (l,r)-Stirling of the first kind.
{"title":"The (l,r)-Stirling numbers: A combinatorial approach","authors":"H. Belbachir, Yahia Djemmada","doi":"10.2298/fil2308587b","DOIUrl":"https://doi.org/10.2298/fil2308587b","url":null,"abstract":"This work deals with a new generalization of r-Stirling numbers using l-tuple of permutations and partitions called (l,r)-Stirling numbers of both kinds. We study various properties of these numbers using combinatorial interpretations and symmetric functions. Also, we give a limit representation of the multiple zeta function using (l,r)-Stirling of the first kind.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68275257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We will introduce and discuss various models of the integrable Teichm?ller space Tp in the real line case, extending some known results on the Weil-Petersson Teichm?ller space T2 to the general space Tp for p > 1.
{"title":"Some notes on integrable Teichmüller space on the real line","authors":"Qingqing Li, Yu-liang Shen","doi":"10.2298/fil2308633l","DOIUrl":"https://doi.org/10.2298/fil2308633l","url":null,"abstract":"We will introduce and discuss various models of the integrable Teichm?ller space Tp in the real line case, extending some known results on the Weil-Petersson Teichm?ller space T2 to the general space Tp for p > 1.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68275566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce the generalized Hahn space hd(p), which is not normable, and show that it is a totally paranormed space. We develop the parametric representation of parts of spheres in three?dimensional space endowed with the relative paranorm of hd(p) and solve the visibility and contour problems for these spheres. Also we apply our own software in line graphics to visualize the shapes of parts of these spheres. Finally we demonstrate the effects of the change of the parameters d and p on the shape of the spheres.
{"title":"Visualization of spheres in the generalized Hahn space","authors":"Vesna Veličković, E. Dolicanin","doi":"10.2298/fil2306701v","DOIUrl":"https://doi.org/10.2298/fil2306701v","url":null,"abstract":"We introduce the generalized Hahn space hd(p), which is not normable, and show that it is a totally paranormed space. We develop the parametric representation of parts of spheres in three?dimensional space endowed with the relative paranorm of hd(p) and solve the visibility and contour problems for these spheres. Also we apply our own software in line graphics to visualize the shapes of parts of these spheres. Finally we demonstrate the effects of the change of the parameters d and p on the shape of the spheres.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68270976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Based on countably irreducible version of Topological Rudin?s Lemma, we give some characterizations of c-sober spaces and ?*-well-filtered spaces. In particular, we prove that a topological space is c-sober iff its Smyth power space is c-sober and a c-sober space is an ?*-well-filtered space. We also show that a locally compact ?+-well-filtered P-space is c-sober and a T0 space X is c-sober iff the one-point compactification of X is c-sober.
{"title":"On c-sober spaces and ω*-well-filtered spaces","authors":"Jinbo Yang, Yun Luo, Zixuan Ye","doi":"10.2298/fil2306989y","DOIUrl":"https://doi.org/10.2298/fil2306989y","url":null,"abstract":"Based on countably irreducible version of Topological Rudin?s Lemma, we give some characterizations of c-sober spaces and ?*-well-filtered spaces. In particular, we prove that a topological space is c-sober iff its Smyth power space is c-sober and a c-sober space is an ?*-well-filtered space. We also show that a locally compact ?+-well-filtered P-space is c-sober and a T0 space X is c-sober iff the one-point compactification of X is c-sober.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68271390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we present the two new kinds of examples of soft quasilinear spaces namely ?gIRn soft interval space? and ?eIs, eIl2, fIl? and fIc0 soft interval sequence spaces?. We give some properties of these spaces. We study completeness of gIRn soft normed quasilinear spaces. Further, we obtain some results on these soft interval spaces and soft interval sequence spaces related to concepts of soft quasilinear dependence-independence and solid-floored.
{"title":"Soft interval spaces and soft interval sequence spaces","authors":"Hacer Bozkurt","doi":"10.2298/fil2309647b","DOIUrl":"https://doi.org/10.2298/fil2309647b","url":null,"abstract":"In this article, we present the two new kinds of examples of soft quasilinear spaces namely ?gIRn soft interval space? and ?eIs, eIl2, fIl? and fIc0 soft interval sequence spaces?. We give some properties of these spaces. We study completeness of gIRn soft normed quasilinear spaces. Further, we obtain some results on these soft interval spaces and soft interval sequence spaces related to concepts of soft quasilinear dependence-independence and solid-floored.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135594430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we investigate the behaviour of the weighted maximal operators of Marcinkiewicz type (C,?)-means ??,* p (f) := supn?P |??n(f)|/ n2/p?(2+?) in the Hardy space Hp(G2) (0 < ? < 1 and p < 2/(2 + ?)). It is showed that the maximal operators ??,* p (f) are bounded from the dyadic Hardy space Hp(G2) to the Lebesgue space Lp(G2), and that this is in a sense sharp. It was also proved a strong convergence theorem for the Marcinkiewicz type (C, ?) means of Walsh-Fourier series in Hp(G2).
本文研究Marcinkiewicz型(C，?)-means ??的加权极大算子的行为。，* p (f):= supn?P | ? ? n (f) | / n2 / P ?(2 +)哈代空间惠普(G2) (0 & lt;？ & lt;1和p <2/(2 + ?))证明了极大算子??，* p(f)从并矢Hardy空间Hp(G2)有界到Lebesgue空间Lp(G2)，这在某种意义上是尖锐的。并在Hp(G2)中证明了Walsh-Fourier级数的Marcinkiewicz型(C， ?)均值的一个强收敛定理。
{"title":"On the weighted maximal operators of Marcinkiewicz type Cesàro means of two-dimensional Walsh-Fourier series","authors":"István Blahota, Károly Nagy","doi":"10.2298/fil2309981b","DOIUrl":"https://doi.org/10.2298/fil2309981b","url":null,"abstract":"In this paper we investigate the behaviour of the weighted maximal operators of Marcinkiewicz type (C,?)-means ??,* p (f) := supn?P |??n(f)|/ n2/p?(2+?) in the Hardy space Hp(G2) (0 < ? < 1 and p < 2/(2 + ?)). It is showed that the maximal operators ??,* p (f) are bounded from the dyadic Hardy space Hp(G2) to the Lebesgue space Lp(G2), and that this is in a sense sharp. It was also proved a strong convergence theorem for the Marcinkiewicz type (C, ?) means of Walsh-Fourier series in Hp(G2).","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135595244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mohammed Khalladi, Marko Kostic, Abdelkader Rahmani, Daniel Velinov
In this paper, we introduce several various classes of (?, c)-almost periodic type functions and their Stepanov generalizations. We also consider the corresponding classes of (?, c)-almost periodic type functions depending on two variables and related composition principles. We provide several illustrative examples and applications to the abstract Volterra integro-differential equations in Banach spaces.
{"title":"(ω,c)-almost periodic type functions and applications","authors":"Mohammed Khalladi, Marko Kostic, Abdelkader Rahmani, Daniel Velinov","doi":"10.2298/fil2302363k","DOIUrl":"https://doi.org/10.2298/fil2302363k","url":null,"abstract":"In this paper, we introduce several various classes of (?, c)-almost periodic type functions and their Stepanov generalizations. We also consider the corresponding classes of (?, c)-almost periodic type functions depending on two variables and related composition principles. We provide several illustrative examples and applications to the abstract Volterra integro-differential equations in Banach spaces.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135685922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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