"In this paper we prove that an interesting result concerning the generalized Hyers-Ulam stability of the linear functional equation $g(varphi(x))=a(x)bullet g(x)$ on a complete metric group, given in 2014 by S.M. Jung, D. Popa and M.T. Rassias, can be obtained using the fixed point technique. Moreover, we give a characterization of the functions that can be approximated with a given error, by the solution of the linear equation mention above. Our results are also related to a recent result of G.H. Kim and Th.M. Rassias concerning the stability of Psi functional equation."
“在本文中，我们证明了一个有趣的结果，关于线性泛函方程$g(varphi(x))=a(x)bullet g(x)$在完备度量群上的广义Hyers-Ulam稳定性，该结果是由S.M. Jung, D. Popa和M.T. Rassias在2014年给出的。此外，我们给出了可以用给定误差近似的函数的一个表征，通过上述线性方程的解。我们的结果也与G.H. Kim和thm.r assias最近关于Psi泛函方程稳定性的结果有关。
{"title":"\"Fixed points and the stability of the linear functional equations in a single variable\"","authors":"L. Cadariu, Laura Manolescu","doi":"10.37193/cjm.2022.03.20","DOIUrl":"https://doi.org/10.37193/cjm.2022.03.20","url":null,"abstract":"\"In this paper we prove that an interesting result concerning the generalized Hyers-Ulam stability of the linear functional equation $g(varphi(x))=a(x)bullet g(x)$ on a complete metric group, given in 2014 by S.M. Jung, D. Popa and M.T. Rassias, can be obtained using the fixed point technique. Moreover, we give a characterization of the functions that can be approximated with a given error, by the solution of the linear equation mention above. Our results are also related to a recent result of G.H. Kim and Th.M. Rassias concerning the stability of Psi functional equation.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48617740","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}
"Orbital fuzzy iterated function systems are obtained as a combination of the concepts of iterated fuzzy set system and orbital iterated function system. It turns out that, for such a system, the corresponding fuzzy operator is weakly Picard, its fixed points being called fuzzy fractals. In this paper we present a structure result concerning fuzzy fractals associated to an orbital fuzzy iterated function system by proving that such an object is perfectly determined by the action of the initial term of the Picard iteration sequence on the closure of the orbits of certain elements."
{"title":"\"A characterization of fuzzy fractals generated by an orbital fuzzy iterated function system\"","authors":"Radu Miculescu, Alexandru Mihail, Irina Savu","doi":"10.37193/cjm.2022.03.06","DOIUrl":"https://doi.org/10.37193/cjm.2022.03.06","url":null,"abstract":"\"Orbital fuzzy iterated function systems are obtained as a combination of the concepts of iterated fuzzy set system and orbital iterated function system. It turns out that, for such a system, the corresponding fuzzy operator is weakly Picard, its fixed points being called fuzzy fractals. In this paper we present a structure result concerning fuzzy fractals associated to an orbital fuzzy iterated function system by proving that such an object is perfectly determined by the action of the initial term of the Picard iteration sequence on the closure of the orbits of certain elements.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43178548","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}
"The purpose of this work is to develop a new version of the extragradient method for solving non-Lipschitzian and pseudo-monotone variational inequalities in real Hilbert spaces. First, we prove a sufficient condition for weak convergence of a proposed algorithm under relaxed assumptions. Next, under strong pseudomonotonicity and Lipschitz continuity assumptions, we obtain also a Q-linear convergence rate of this algorithm. Our results improve some recent contributions in the literature on the extragradient method."
{"title":"\"Extragradient method with a new adaptive step size for solving non-Lipschitzian pseudo-monotone variational inequalities\"","authors":"Duong Viet Thong","doi":"10.37193/cjm.2022.02.19","DOIUrl":"https://doi.org/10.37193/cjm.2022.02.19","url":null,"abstract":"\"The purpose of this work is to develop a new version of the extragradient method for solving non-Lipschitzian and pseudo-monotone variational inequalities in real Hilbert spaces. First, we prove a sufficient condition for weak convergence of a proposed algorithm under relaxed assumptions. Next, under strong pseudomonotonicity and Lipschitz continuity assumptions, we obtain also a Q-linear convergence rate of this algorithm. Our results improve some recent contributions in the literature on the extragradient method.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49147559","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}
A. Ibrahim, P. Kumam, A. Abubakar, Jamilu Abubakar
"Many real-world phenomena in engineering, economics, statistical inference, compressed sensing and machine learning involve finding sparse solutions to under-determined or ill-conditioned equations. Our interest in this paper is to introduce a derivative-free method for recovering sparse signal and blurred image arising in compressed sensing by solving a nonlinear equation involving a monotone operator. The global convergence of the proposed method is established under the assumptions of monotonicity and Lipschitz continuity of the underlying operator. Numerical experiments are performed to illustrate the efficiency of the proposed method in the reconstruction of sparse signals and blurred images."
{"title":"\"A descent three-term derivative-free method for signal reconstruction in compressive sensing\"","authors":"A. Ibrahim, P. Kumam, A. Abubakar, Jamilu Abubakar","doi":"10.37193/cjm.2022.02.13","DOIUrl":"https://doi.org/10.37193/cjm.2022.02.13","url":null,"abstract":"\"Many real-world phenomena in engineering, economics, statistical inference, compressed sensing and machine learning involve finding sparse solutions to under-determined or ill-conditioned equations. Our interest in this paper is to introduce a derivative-free method for recovering sparse signal and blurred image arising in compressed sensing by solving a nonlinear equation involving a monotone operator. The global convergence of the proposed method is established under the assumptions of monotonicity and Lipschitz continuity of the underlying operator. Numerical experiments are performed to illustrate the efficiency of the proposed method in the reconstruction of sparse signals and blurred images.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44229256","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 article considers a split generalized equilibrium problem and fixed point problem for infi- nite family of nonexpansive mapping in Hilbert space. We propose an algorithm for finding a common solution of these problems. Under mild assumptions, we establish a strong convergence theorem for the sequence gen- erated by the proposed algorithm using viscosity technique. We present the implementation of the proposed algorithm by considering some numerical illustrations and comparison of the proposed algorithm with an ex- isting algorithm in the literature."
{"title":"\"Viscosity algorithm for solving split generalized equilibrium problem and fixed-point problem\"","authors":"Jamilu Abubakar, Jitsupa Deepho","doi":"10.37193/cjm.2022.02.01","DOIUrl":"https://doi.org/10.37193/cjm.2022.02.01","url":null,"abstract":"\"This article considers a split generalized equilibrium problem and fixed point problem for infi- nite family of nonexpansive mapping in Hilbert space. We propose an algorithm for finding a common solution of these problems. Under mild assumptions, we establish a strong convergence theorem for the sequence gen- erated by the proposed algorithm using viscosity technique. We present the implementation of the proposed algorithm by considering some numerical illustrations and comparison of the proposed algorithm with an ex- isting algorithm in the literature.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43553086","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 prove an identity theorem for Gˆateaux holomorphic functions on polygonally connected 2- open sets, which yields a very general maximum norm principle and a sublinear “max-min” principle. All results apply in particular to vector-valued functions which are holomorphic (in any sense that implies Gˆateaux holomorphy) on domains in Hausdorff locally convex spaces."
{"title":"\"On the maximum modulus principle and the identity theorem in arbitrary dimension\"","authors":"Vlad Timofte","doi":"10.37193/cjm.2022.02.20","DOIUrl":"https://doi.org/10.37193/cjm.2022.02.20","url":null,"abstract":"\"We prove an identity theorem for Gˆateaux holomorphic functions on polygonally connected 2- open sets, which yields a very general maximum norm principle and a sublinear “max-min” principle. All results apply in particular to vector-valued functions which are holomorphic (in any sense that implies Gˆateaux holomorphy) on domains in Hausdorff locally convex spaces.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48268230","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, a first-order iterative functional differential equation is investigated. With the help of the Schauder’s fixed point theorem, we established some sufficient criteria that ensure the existence of positive periodic solutions. In addition, an application to three hematopoiesis models is also provided to corroborate the effeteness of our main findings. These last ones substantially enrich and complement some earlier works."
{"title":"\"Positive periodic solutions for a class of first-order iterative differential equations with an application to a hematopoiesis model\"","authors":"Ahlème Bouakkaz","doi":"10.37193/cjm.2022.02.07","DOIUrl":"https://doi.org/10.37193/cjm.2022.02.07","url":null,"abstract":"\"In this paper, a first-order iterative functional differential equation is investigated. With the help of the Schauder’s fixed point theorem, we established some sufficient criteria that ensure the existence of positive periodic solutions. In addition, an application to three hematopoiesis models is also provided to corroborate the effeteness of our main findings. These last ones substantially enrich and complement some earlier works.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43366721","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}
G. Chatzarakis, N. Indrajith, S. Panetsos, E. Thandapani
"This paper introduces a new improved method for obtaining the oscillation of a second-order advanced difference equation of the form begin{equation*} Delta(eta(n)Deltachi(n))+f(n)chi(sigma(n))=0 end{equation*} where $eta(n)>0,$ $sum_{n=n_0}^{infty}frac{1}{eta(n)}0,$ $sigma(n)geq n+1,$ and ${sigma(n)}$ is a monotonically increasing integer sequence. We derive new oscillation criteria by transforming the studied equation into the canonical form. The obtained results are original and improve on the existing criteria. Examples illustrating the main results are presented at the end of the paper."
{"title":"\"Oscillations of second-order noncanonical advanced difference equations via canonical transformation\"","authors":"G. Chatzarakis, N. Indrajith, S. Panetsos, E. Thandapani","doi":"10.37193/cjm.2022.02.09","DOIUrl":"https://doi.org/10.37193/cjm.2022.02.09","url":null,"abstract":"\"This paper introduces a new improved method for obtaining the oscillation of a second-order advanced difference equation of the form begin{equation*} Delta(eta(n)Deltachi(n))+f(n)chi(sigma(n))=0 end{equation*} where $eta(n)>0,$ $sum_{n=n_0}^{infty}frac{1}{eta(n)}<infty,$ $f(n)>0,$ $sigma(n)geq n+1,$ and ${sigma(n)}$ is a monotonically increasing integer sequence. We derive new oscillation criteria by transforming the studied equation into the canonical form. The obtained results are original and improve on the existing criteria. Examples illustrating the main results are presented at the end of the paper.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48904012","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}
"The paper compares four variants of algorithms that solve the problem of Convex Feasibility using affine combinations of projections, two classical variants of Parallel Projection Method (PPM) and two modified variants that involve variable weight, in terms of their effectiveness in inpainting a convex polygon, as well as in terms of their convergence in a finite a number of step. We also present a numerical study of the dependence of the efficiency and the execution speed of these algorithms on the shape of the inpainted convex set, as well as on the values of the relaxation parameter."
{"title":"\"A visual and numerical comparative study of some parallel affine projection algorithms for solving the convex feasibility problem with application to scratch inpainting\"","authors":"Irina Maria Artinescu, C. Boldea","doi":"10.37193/cjm.2022.02.03","DOIUrl":"https://doi.org/10.37193/cjm.2022.02.03","url":null,"abstract":"\"The paper compares four variants of algorithms that solve the problem of Convex Feasibility using affine combinations of projections, two classical variants of Parallel Projection Method (PPM) and two modified variants that involve variable weight, in terms of their effectiveness in inpainting a convex polygon, as well as in terms of their convergence in a finite a number of step. We also present a numerical study of the dependence of the efficiency and the execution speed of these algorithms on the shape of the inpainted convex set, as well as on the values of the relaxation parameter.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46648077","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 shall study the existence and approximation results for a nonlinear two point boundary value problem of a second order ordinary differential equation with general form of Dirichlet/Neumann type boundary conditions. The nonlinearity present on right hand side of the differential equation is assumed to be Caratho´eodory containing a deviating argument. The proofs of the main results are based on a monotone iteration method contained in the hybrid fixed point principles of Dhage (2014) in an ordered Banach space. Finally, some remarks concerning the merits of our monotone iteration method over other frequently used iteration methods in the theory of nonlinear differential equations are given in the conclusion."
{"title":"\"Monotone iteration method for general nonlinear two point boundary value problems with deviating arguments\"","authors":"B. Dhage, Janhavi B. Dhage, J. Ali","doi":"10.37193/cjm.2022.02.11","DOIUrl":"https://doi.org/10.37193/cjm.2022.02.11","url":null,"abstract":"\"In this paper we shall study the existence and approximation results for a nonlinear two point boundary value problem of a second order ordinary differential equation with general form of Dirichlet/Neumann type boundary conditions. The nonlinearity present on right hand side of the differential equation is assumed to be Caratho´eodory containing a deviating argument. The proofs of the main results are based on a monotone iteration method contained in the hybrid fixed point principles of Dhage (2014) in an ordered Banach space. Finally, some remarks concerning the merits of our monotone iteration method over other frequently used iteration methods in the theory of nonlinear differential equations are given in the conclusion.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41688691","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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