Pub Date : 2023-06-26DOI: 10.15330/cmp.15.1.158-179
G. C. Ugwunnadi, L. Y. Haruna, M. Harbau
In this paper, a new accelerated extrapolation Krasnoselski-Mann type algorithm for finding common element in the solution set of the hierarchical fixed point and split monotone variational inclusion problems are introduced in the setting of a real Hilbert space. We then prove that a sequence generated by the algorithm converges strongly to such common element which also approximates solution of some fixed point problem of demimetric mapping in the space. Finally, some applications and numerical experiment are given to show effectiveness of the proposed algorithm over the recently known related results in the literature. The established results extend and generalize many recent ones announced in the literature.
{"title":"Accelerated Krasnoselski-Mann type algorithm for hierarchical fixed point and split monotone variational inclusion problems in Hilbert spaces","authors":"G. C. Ugwunnadi, L. Y. Haruna, M. Harbau","doi":"10.15330/cmp.15.1.158-179","DOIUrl":"https://doi.org/10.15330/cmp.15.1.158-179","url":null,"abstract":"In this paper, a new accelerated extrapolation Krasnoselski-Mann type algorithm for finding common element in the solution set of the hierarchical fixed point and split monotone variational inclusion problems are introduced in the setting of a real Hilbert space. We then prove that a sequence generated by the algorithm converges strongly to such common element which also approximates solution of some fixed point problem of demimetric mapping in the space. Finally, some applications and numerical experiment are given to show effectiveness of the proposed algorithm over the recently known related results in the literature. The established results extend and generalize many recent ones announced in the literature.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"8 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84269997","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 : 2023-06-22DOI: 10.15330/cmp.15.1.137-149
P. Kórus, J. N. Nápoles Valdés
In this paper, we present some new integral inequalities of Hermite-Hadamard type. To obtain these results, general convex functions of various type are considered such as $(h,m)$-convex functions. The main results extend some previously known inequalities by taking fractional integral operators.
{"title":"On some integral inequalities for $(h,m)$-convex functions in a generalized framework","authors":"P. Kórus, J. N. Nápoles Valdés","doi":"10.15330/cmp.15.1.137-149","DOIUrl":"https://doi.org/10.15330/cmp.15.1.137-149","url":null,"abstract":"In this paper, we present some new integral inequalities of Hermite-Hadamard type. To obtain these results, general convex functions of various type are considered such as $(h,m)$-convex functions. The main results extend some previously known inequalities by taking fractional integral operators.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"27 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76956182","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 : 2023-06-21DOI: 10.15330/cmp.15.1.128-136
V. Karakaya, D. Sekman
It is well known that the Banach contraction principle implies the existence of fixed points of single-valued mappings. On the other hand, S.B. Nadler has solved the problem that guarantees the existence of fixed point for multivalued mapping. However, we have to emphasize that similar methods are not applied for nonexpansive multivalued mappings. The aim of this study is to investigate the existence of a fixed point on nonexpansive multivalued mappings with the help of function sequences and functions having shifting distance property. In addition, some hypothesis of this work were explained with an interesting example.
{"title":"On fixed points of some multivalued mappings under certain function classes","authors":"V. Karakaya, D. Sekman","doi":"10.15330/cmp.15.1.128-136","DOIUrl":"https://doi.org/10.15330/cmp.15.1.128-136","url":null,"abstract":"It is well known that the Banach contraction principle implies the existence of fixed points of single-valued mappings. On the other hand, S.B. Nadler has solved the problem that guarantees the existence of fixed point for multivalued mapping. However, we have to emphasize that similar methods are not applied for nonexpansive multivalued mappings. The aim of this study is to investigate the existence of a fixed point on nonexpansive multivalued mappings with the help of function sequences and functions having shifting distance property. In addition, some hypothesis of this work were explained with an interesting example.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"61 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78321119","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 : 2023-06-20DOI: 10.15330/cmp.15.1.104-119
Vasylyshyn S.I
We consider the subalgebra of the Fréchet algebra of entire functions of bounded type, generated by a countable set of algebraically independent homogeneous polynomials on the complex Banach space $X.$ We investigate the spectrum of this subalgebra in the case $X = ell_1.$ We also consider some shift type operations that can be performed on the spectrum of this subalgebra in the case $X = ell_p$ with $p geq 1$.
{"title":"Spectra of algebras of analytic functions, generated by sequences of polynomials on Banach spaces, and operations on spectra","authors":"Vasylyshyn S.I","doi":"10.15330/cmp.15.1.104-119","DOIUrl":"https://doi.org/10.15330/cmp.15.1.104-119","url":null,"abstract":"We consider the subalgebra of the Fréchet algebra of entire functions of bounded type, generated by a countable set of algebraically independent homogeneous polynomials on the complex Banach space $X.$ We investigate the spectrum of this subalgebra in the case $X = ell_1.$ We also consider some shift type operations that can be performed on the spectrum of this subalgebra in the case $X = ell_p$ with $p geq 1$.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"35 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75136679","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 : 2023-06-20DOI: 10.15330/cmp.15.1.120-127
F. Mofarreh, DE U.C.
The aim of this article is to characterize a Kenmotsu 3-manifold whose metric is either a gradient Yamabe soliton or gradient Einstein soliton. It is proven that in both cases this manifold is reduced to the manifold of constant sectional curvature. Finally, we verify the obtained results by an example.
{"title":"Kenmotsu 3-manifolds and gradient solitons","authors":"F. Mofarreh, DE U.C.","doi":"10.15330/cmp.15.1.120-127","DOIUrl":"https://doi.org/10.15330/cmp.15.1.120-127","url":null,"abstract":"The aim of this article is to characterize a Kenmotsu 3-manifold whose metric is either a gradient Yamabe soliton or gradient Einstein soliton. It is proven that in both cases this manifold is reduced to the manifold of constant sectional curvature. Finally, we verify the obtained results by an example.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"24 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72900133","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 : 2023-06-19DOI: 10.15330/cmp.15.2.563-575
V. Babenko, V. Babenko, O. Kovalenko, N. Parfinovych
We obtain a sharp Nagy type inequality in a metric space $(X,rho)$ with measure $mu$ that estimates the uniform norm of a function using its $|cdot|_{H^omega}$-norm determined by a modulus of continuity $omega$, and a seminorm that is defined on a space of locally integrable functions. We consider charges $nu$ that are defined on the set of $mu$-measurable subsets of $X$ and are absolutely continuous with respect to $mu$. Using the obtained Nagy type inequality, we prove a sharp Landau-Kolmogorov type inequality that estimates the uniform norm of a Radon-Nikodym derivative of a charge via a $|cdot|_{H^omega}$-norm of this derivative, and a seminorm defined on the space of such charges. We also prove a sharp inequality for a hypersingular integral operator. In the case $X={mathbb R}_+^mtimes {mathbb R}^{d-m}$, $0le mle d$, we obtain inequalities that estimate the uniform norm of a mixed derivative of a function using the uniform norm of the function and the $|cdot|_{H^omega}$-norm of its mixed derivative.
{"title":"Nagy type inequalities in metric measure spaces and some applications","authors":"V. Babenko, V. Babenko, O. Kovalenko, N. Parfinovych","doi":"10.15330/cmp.15.2.563-575","DOIUrl":"https://doi.org/10.15330/cmp.15.2.563-575","url":null,"abstract":"We obtain a sharp Nagy type inequality in a metric space $(X,rho)$ with measure $mu$ that estimates the uniform norm of a function using its $|cdot|_{H^omega}$-norm determined by a modulus of continuity $omega$, and a seminorm that is defined on a space of locally integrable functions. We consider charges $nu$ that are defined on the set of $mu$-measurable subsets of $X$ and are absolutely continuous with respect to $mu$. Using the obtained Nagy type inequality, we prove a sharp Landau-Kolmogorov type inequality that estimates the uniform norm of a Radon-Nikodym derivative of a charge via a $|cdot|_{H^omega}$-norm of this derivative, and a seminorm defined on the space of such charges. We also prove a sharp inequality for a hypersingular integral operator. In the case $X={mathbb R}_+^mtimes {mathbb R}^{d-m}$, $0le mle d$, we obtain inequalities that estimate the uniform norm of a mixed derivative of a function using the uniform norm of the function and the $|cdot|_{H^omega}$-norm of its mixed derivative.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"58 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139369479","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 : 2023-06-18DOI: 10.15330/cmp.15.1.95-103
H. Altin
This paper is an introduction to a sequence of nonlinear Baskakov-Durrmeyer operators $(NBD_{n})$ of the form [ (NBD_{n})(f;x) =int_{0}^infty K_{n}(x,t,f(t)),dt ] with $xin [0,infty)$ and $ninmathbb{N}$. While $K_{n}(x,t,u)$ provide convenient assumptions, these operators work on bounded functions, which are defined on all finite subintervals of $[0,infty)$. This paper comprise some pointwise convergence results for these operators in certain functional spaces. As well as this study can be seen as a continuation of studies about nonlinear operators, it is the first study on nonlinear Baskakov-Durrmeyer or modified Baskakov operators, while there were more papers on linear part of the operators.
{"title":"Some convergence results for nonlinear Baskakov-Durrmeyer operators","authors":"H. Altin","doi":"10.15330/cmp.15.1.95-103","DOIUrl":"https://doi.org/10.15330/cmp.15.1.95-103","url":null,"abstract":"This paper is an introduction to a sequence of nonlinear Baskakov-Durrmeyer operators $(NBD_{n})$ of the form [ (NBD_{n})(f;x) =int_{0}^infty K_{n}(x,t,f(t)),dt ] with $xin [0,infty)$ and $ninmathbb{N}$. While $K_{n}(x,t,u)$ provide convenient assumptions, these operators work on bounded functions, which are defined on all finite subintervals of $[0,infty)$. This paper comprise some pointwise convergence results for these operators in certain functional spaces. As well as this study can be seen as a continuation of studies about nonlinear operators, it is the first study on nonlinear Baskakov-Durrmeyer or modified Baskakov operators, while there were more papers on linear part of the operators.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"31 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81776310","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}
A. Romanyuk, V. Romanyuk, K. Pozharska, S. Hembars’ka
Exact order estimates for some characteristics of linear and nonlinear approximation of the isotropic Nikol'skii-Besov classes $mathbf{B}^r_{p,theta}$ of periodic multivariate functions in the spaces $B_{q,1}$, $1leq q leq infty$, are obtained. Among them are the best orthogonal trigonometric approximations, best $m$-term trigonometric approximations, Kolmogorov, linear and trigonometric widths. For all considered characteristics, their estimates coincide in order with the corresponding estimates in the spaces $L_{q}$. Moreover, the obtained exact in order estimates (except the case $1
{"title":"Characteristics of linear and nonlinear approximation of isotropic classes of periodic multivariate functions","authors":"A. Romanyuk, V. Romanyuk, K. Pozharska, S. Hembars’ka","doi":"10.15330/cmp.15.1.78-94","DOIUrl":"https://doi.org/10.15330/cmp.15.1.78-94","url":null,"abstract":"Exact order estimates for some characteristics of linear and nonlinear approximation of the isotropic Nikol'skii-Besov classes $mathbf{B}^r_{p,theta}$ of periodic multivariate functions in the spaces $B_{q,1}$, $1leq q leq infty$, are obtained. Among them are the best orthogonal trigonometric approximations, best $m$-term trigonometric approximations, Kolmogorov, linear and trigonometric widths. \u0000For all considered characteristics, their estimates coincide in order with the corresponding estimates in the spaces $L_{q}$. Moreover, the obtained exact in order estimates (except the case $1<p<2leq q < frac{p}{p-1}$) are realized by the approximation of functions from the classes ${mathbf{B}}^r_{p,theta}$ by trigonometric polynomials with the spectrum in cubic regions. In any case, they do not depend on the smoothness parameter $theta$.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"18 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75731907","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}
The crossing number $mathrm{cr}(G)$ of a graph $G$ is the minimum number of edge crossings over all drawings of $G$ in the plane. The main aim of this paper is to give the crossing numbers of the join products of eight graphs on six vertices with paths and cycles on $n$ vertices. The proofs are done with the help of several well-known auxiliary statements, the idea of which is extended by a suitable classification of subgraphs that do not cross the edges of the examined graphs.
{"title":"The crossing numbers of join products of eight graphs of order six with paths and cycles","authors":"M. Staš","doi":"10.15330/cmp.15.1.66-77","DOIUrl":"https://doi.org/10.15330/cmp.15.1.66-77","url":null,"abstract":"The crossing number $mathrm{cr}(G)$ of a graph $G$ is the minimum number of edge crossings over all drawings of $G$ in the plane. The main aim of this paper is to give the crossing numbers of the join products of eight graphs on six vertices with paths and cycles on $n$ vertices. The proofs are done with the help of several well-known auxiliary statements, the idea of which is extended by a suitable classification of subgraphs that do not cross the edges of the examined graphs.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"377 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80607498","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}
The coefficient inverse problem for the degenerate parabolic equation is investigated. The minor coefficient of this equation is the polynomial of the first power with respect to the space variable with two unknown time-dependent functions. The investigation is carried out under given inhomogeneous initial condition, Dirichlet boundary conditions and integral overdetermination conditions. We establish the conditions of the unique solvability to the named problem for the case of strong degeneration.
{"title":"Coefficient inverse problem for the strongly degenerate parabolic equation","authors":"N. Huzyk, P. Pukach, M. Vovk","doi":"10.15330/cmp.15.1.52-65","DOIUrl":"https://doi.org/10.15330/cmp.15.1.52-65","url":null,"abstract":"The coefficient inverse problem for the degenerate parabolic equation is investigated. The minor coefficient of this equation is the polynomial of the first power with respect to the space variable with two unknown time-dependent functions. The investigation is carried out under given inhomogeneous initial condition, Dirichlet boundary conditions and integral overdetermination conditions. We establish the conditions of the unique solvability to the named problem for the case of strong degeneration.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"270 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79898435","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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