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Carpathian Journal of Mathematics最新文献

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A New Accelerated Viscosity Forward-backward Algorithm with a Linesearch for Some Convex Minimization Problems and its Applications to Data Classification 一种新的带直线的加速黏度正向倒向算法求解一些凸最小化问题及其在数据分类中的应用
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-30 DOI: 10.37193/cjm.2023.01.08
Dawan Chumpungam, Panitarn Sarnmeta, S. Suantai
{"title":"A New Accelerated Viscosity Forward-backward Algorithm with a Linesearch for Some Convex Minimization Problems and its Applications to Data Classification","authors":"Dawan Chumpungam, Panitarn Sarnmeta, S. Suantai","doi":"10.37193/cjm.2023.01.08","DOIUrl":"https://doi.org/10.37193/cjm.2023.01.08","url":null,"abstract":"\" In this paper, we focus on solving convex minimization problem in the form of a summation of two convex functions in which one of them is Frec'{e}t differentiable. In order to solve this problem, we introduce a new accelerated viscosity forward-backward algorithm with a new linesearch technique. The proposed algorithm converges strongly to a solution of the problem without assuming that a gradient of the objective function is $L$-Lipschitz continuous. As applications, we apply the proposed algorithm to classification problems and compare its performance with other algorithms mentioned in the literature. \"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47762300","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}
引用次数: 0
Geometric inequalities in real Banach spaces with applications 实Banach空间中的几何不等式及其应用
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-30 DOI: 10.37193/cjm.2023.01.07
C. E. Chidume
{"title":"Geometric inequalities in real Banach spaces with applications","authors":"C. E. Chidume","doi":"10.37193/cjm.2023.01.07","DOIUrl":"https://doi.org/10.37193/cjm.2023.01.07","url":null,"abstract":"\"In this paper, new geometric inequalities are established in real Banach spaces. As an application, a new iterative algorithm is proposed for approximating a solution of a split equality fixed point problem (SEFPP) for a quasi-$phi$-nonexpansive semigroup. It is proved that the sequence generated by the algorithm converges {it strongly} to a solution of the SEFPP in $p$-uniformly convex and uniformly smooth real Banach spaces, $p>1$. Furthermore, the theorem proved is applied to approximate a solution of a variational inequality problem. All the theorems proved are applicable, in particular, in $L_p$, $l_p$ and the Sobolev spaces, $W_p^m(Omega)$, for $p$ such that $2","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46374591","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}
引用次数: 0
Inertial Iteration Scheme for Approximating Fixed Points of Lipschitz Pseudocontractive Maps in Arbitrary Real Banach Spaces 逼近任意实Banach空间中Lipschitz伪压缩映射不动点的惯性迭代格式
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-30 DOI: 10.37193/cjm.2023.01.13
P. U. Nwokoro, D. F. Agbebaku, E. E. Chima, A. C. Onah, O. Oguguo, M. Osilike
{"title":"Inertial Iteration Scheme for Approximating Fixed Points of Lipschitz Pseudocontractive Maps in Arbitrary Real Banach Spaces","authors":"P. U. Nwokoro, D. F. Agbebaku, E. E. Chima, A. C. Onah, O. Oguguo, M. Osilike","doi":"10.37193/cjm.2023.01.13","DOIUrl":"https://doi.org/10.37193/cjm.2023.01.13","url":null,"abstract":"\"We study a perturbed inertial Krasnoselskii-Mann-type algorithm and prove that the algorithm is an approximate fixed point sequence for Lipschitz pseudocontractive maps in arbitrary real Banach spaces. Strong convergence results are then established for our inertial iteration scheme for approximation of fixed points of Lipschitz pseudocontractive maps and solutions of certain important accretive-type operator equations in certain real Banach spaces. Implementation of our algorithm is illustrated using numerical examples in both finite and infinite dimensional Banach spaces. Our results improve rate of convergence and extend several related recent results. \"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47000603","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}
引用次数: 0
The affine Orlicz log-Minkowki inequality 仿射Orlicz-log-Minkowki不等式
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-30 DOI: 10.37193/cjm.2023.01.20
Chang-Jian Zhao
{"title":"The affine Orlicz log-Minkowki inequality","authors":"Chang-Jian Zhao","doi":"10.37193/cjm.2023.01.20","DOIUrl":"https://doi.org/10.37193/cjm.2023.01.20","url":null,"abstract":"In this paper, we establish an affine Orlicz log-Minkowki inequality for the affine quermassintegrals by introducing new concepts of affine measures and Orlicz mixed affine measures, and using the newly established Orlicz affine Minkowski inequality for the affine quermassintegrals. The affine Orlicz log-Minkowski inequality in special case yields $L_{p}$-affine log-Minkowski inequality. The affine log-Minkowski inequality is also derived.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45376464","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}
引用次数: 0
"Approximating fixed points of demicontractive mappings via the quasi-nonexpansive case" “通过拟非扩张情形逼近半压缩映射的不动点”
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-30 DOI: 10.37193/cjm.2023.01.04
V. Berinde
{"title":"\"Approximating fixed points of demicontractive mappings via the quasi-nonexpansive case\"","authors":"V. Berinde","doi":"10.37193/cjm.2023.01.04","DOIUrl":"https://doi.org/10.37193/cjm.2023.01.04","url":null,"abstract":"\"We prove that the convergence theorems for Mann iteration used for approximation of the fixed points of demicontractive mappings in Hilbert spaces can be derived from the corresponding convergence theorems in the class of quasi-nonexpansive mappings. Our derivation is based on an important auxiliary lemma (Lemma ref{lem3}), which shows that if $T$ is $k$-demicontractive, then for any $lambdain (0,1-k)$, $T_{lambda}$ is quasi-nonexpansive. In this way we obtain a unifying technique of proof for various well known results in the fixed point theory of demicontractive mappings. We illustrate this reduction technique for the case of two classical convergence results in the class of demicontractive mappings: [Mu aruc ster, c St. The solution by iteration of nonlinear equations in Hilbert spaces. {em Proc. Amer. Math. Soc.} {bf 63} (1977), no. 1, 69--73] and [Hicks, T. L.; Kubicek, J. D. On the Mann iteration process in a Hilbert space. {em J. Math. Anal. Appl.} {bf 59} (1977), no. 3, 498--504].\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49636264","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}
引用次数: 2
A Hybrid Steepest-Descent Algorithm for Convex Minimization Over the Fixed Point Set of Multivalued Mappings 多值映射不动点集凸最小化的混合最陡下降算法
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-30 DOI: 10.37193/cjm.2023.01.21
Yasir Arfat, P. Kumam, M. A. A. Khan, Y. Cho
{"title":"A Hybrid Steepest-Descent Algorithm for Convex Minimization Over the Fixed Point Set of Multivalued Mappings","authors":"Yasir Arfat, P. Kumam, M. A. A. Khan, Y. Cho","doi":"10.37193/cjm.2023.01.21","DOIUrl":"https://doi.org/10.37193/cjm.2023.01.21","url":null,"abstract":"In the setting of Hilbert spaces, we show that a hybrid steepest-descent algorithm converges strongly to a solution of a convex minimization problem over the fixed point set of a finite family of multivalued demicontractive mappings. We also provide numerical results concerning the viability of the proposed algorithm with possible applications.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49231755","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}
引用次数: 0
Modified inertial Mann’s algorithm and inertial hybrid 改进的惯性Mann算法与惯性混合
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-30 DOI: 10.37193/cjm.2023.01.02
Suparat Baiya, K. Ungchittrakool
{"title":"Modified inertial Mann’s algorithm and inertial hybrid","authors":"Suparat Baiya, K. Ungchittrakool","doi":"10.37193/cjm.2023.01.02","DOIUrl":"https://doi.org/10.37193/cjm.2023.01.02","url":null,"abstract":"\"In this work, we introduce and study the modified inertial Mann’s algorithm and inertial hybrid algorithm for approximating some fixed points of a k-strict pseudo-contractive mapping in Hilbert spaces. Weak convergence to a solution of fixed-point problems for a k-strict pseudo-contractive mapping is obtained by using the modified inertial Mann’s algorithm. In order to obtain strong convergence, we introduce an inertial hybrid algorithm by using the inertial extrapolation method mixed with the convex combination of three iterated vectors and forcing for strong convergence by the hybrid projection method for a k-strict pseudo-contractive mapping in Hilbert spaces. The strong convergence theorem of the proposed method is proved under mild assumptions on the scalars. For illustrating the performance of the proposed algorithms, we provide some new nonlinear k-strict pseudo-contractive mappings which are not nonexpansive to create some numerical experiments to show the advantage of the two new inertial algorithms for a k-strict pseudo-contractive mapping.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46150594","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}
引用次数: 0
Stepsize Choice for Korpelevich's and Popov's Extragradient Algorithms for Convex-Concave Minimax Problems 凸凹极大极小问题的Korpelevich和Popov超梯度算法的步长选择
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-30 DOI: 10.37193/cjm.2023.01.22
Jiaojiao Wang, H. Xu
{"title":"Stepsize Choice for Korpelevich's and Popov's Extragradient Algorithms for Convex-Concave Minimax Problems","authors":"Jiaojiao Wang, H. Xu","doi":"10.37193/cjm.2023.01.22","DOIUrl":"https://doi.org/10.37193/cjm.2023.01.22","url":null,"abstract":"\"We show that the choice of stepsize in Korpelevich's extragradient algorithm is sharp, while the choice of stepsize in Popov's extragradient algorithm can be relaxed. We also extend Korpelevich's extragradient algorithm and Popov's extragradient algorithm (with larger stepsize) to the infinite-dimensional Hilbert space framework, with weak convergence.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46847545","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}
引用次数: 0
On Fixed Points of Enriched Contractions and Enriched Nonexpansive Mappings 关于富压缩和富非扩张映射的不动点
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-30 DOI: 10.37193/cjm.2023.01.16
S. Salisu, P. Kumam, Songpon Sriwongsa
{"title":"On Fixed Points of Enriched Contractions and Enriched Nonexpansive Mappings","authors":"S. Salisu, P. Kumam, Songpon Sriwongsa","doi":"10.37193/cjm.2023.01.16","DOIUrl":"https://doi.org/10.37193/cjm.2023.01.16","url":null,"abstract":"We apply the concept of quasilinearization to introduce some enriched classes of Banach contraction mappings and analyse the fixed points of such mappings in the setting of Hadamard spaces. We establish existence and uniqueness of the fixed point of such mappings. To approximate the fixed points, we use an appropriate Krasnoselskij-type scheme for which we establish $Delta$ and strong convergence theorems. Furthermore, we discuss the fixed points of local enriched contractions and Maia-type enriched contractions in Hadamard spaces setting. In addition, we establish demiclosedness-type property of enriched nonexpansive mappings. Finally, we present some special cases and corresponding fixed point theorems.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44819754","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}
引用次数: 2
On normalized distance Laplacian eigenvalues of graphs and applications to graphs defined on groups and rings 关于图的归一化距离拉普拉斯特征值及其在群和环上定义图中的应用
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-30 DOI: 10.37193/cjm.2023.01.14
B. Rather, H. A. Ganie, M. Aouchiche
{"title":"On normalized distance Laplacian eigenvalues of graphs and applications to graphs defined on groups and rings","authors":"B. Rather, H. A. Ganie, M. Aouchiche","doi":"10.37193/cjm.2023.01.14","DOIUrl":"https://doi.org/10.37193/cjm.2023.01.14","url":null,"abstract":"The normalized distance Laplacian matrix of a connected graph $ G $, denoted by $ D^{mathcal{L}}(G) $, is defined by $ D^{mathcal{L}}(G)=Tr(G)^{-1/2}D^L(G)Tr(G)^{-1/2}, $ where $ D(G) $ is the distance matrix, the $D^{L}(G)$ is the distance Laplacian matrix and $ Tr(G)$ is the diagonal matrix of vertex transmissions of $ G. $ The set of all eigenvalues of $ D^{mathcal{L}}(G) $ including their multiplicities is the normalized distance Laplacian spectrum or $ D^{mathcal{L}} $-spectrum of $G$. In this paper, we find the $ D^{mathcal{L}} $-spectrum of the joined union of regular graphs in terms of the adjacency spectrum and the spectrum of an auxiliary matrix. As applications, we determine the $ D^{mathcal{L}} $-spectrum of the graphs associated with algebraic structures. In particular, we find the $ D^{mathcal{L}} $-spectrum of the power graphs of groups, the $ D^{mathcal{L}} $-spectrum of the commuting graphs of non-abelian groups and the $ D^{mathcal{L}} $-spectrum of the zero-divisor graphs of commutative rings. Several open problems are given for further work.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46827457","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}
引用次数: 2
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