The aim of this paper is to introduce two notions of Levitin$-$Polyak (LP in short) well-posedness for a parametric set optimization problem, a pointwise and a global notion. Necessary and sufficient conditions for a parametric set optimization problem to be LP well-posed are given. Characterizations of LP well-posedness for a parametric set optimization problem in terms of upper Hausdorff convergence and Painlev'{e}$-$Kuratowski convergence of sequences of approximate solution sets are also established.
{"title":"Levitin-Polyak Well-Posedness for Parametric Set Optimization Problem","authors":"Biswajit Tahu, M. Dhingra, Shylendra Kumar","doi":"10.37193/cjm.2023.02.12","DOIUrl":"https://doi.org/10.37193/cjm.2023.02.12","url":null,"abstract":"The aim of this paper is to introduce two notions of Levitin$-$Polyak (LP in short) well-posedness for a parametric set optimization problem, a pointwise and a global notion. Necessary and sufficient conditions for a parametric set optimization problem to be LP well-posed are given. Characterizations of LP well-posedness for a parametric set optimization problem in terms of upper Hausdorff convergence and Painlev'{e}$-$Kuratowski convergence of sequences of approximate solution sets are also established.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46099154","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}
Recently Berinde and Păcurar [Approximating fixed points of enriched contractions in Banach spaces. {em J. Fixed Point Theory Appl.} {bf 22} (2020), no. 2., 1--10], first introduced the idea of enriched contraction mappings and proved the existence of a fixed point of an enriched contraction mapping using the well-known fact that any fixed point of {the averaged mapping $T_lambda$, where $lambdain (0,1]$, is also a fixed point of the initial mapping $T$}. In this work, we introduce the idea of weak enriched contraction mappings, and a new generalization of an averaged mapping called double averaged mapping. The first attempt is to prove the existence and uniqueness of the fixed point of a double averaged mapping associated with a weak enriched contraction mapping. Based on this result on Banach spaces, we give some sufficient conditions for the equality of all fixed points of a double averaged mapping and the set {of all fixed points of a weak enriched contraction mapping.} Moreover, our results show that an appropriate Kirk's iterative algorithm can be used to approximate a fixed point of a weak enriched contraction mapping. An illustrative example for showing the efficiency of our results is given.
{"title":"On approximating fixed points of weak enriched contraction mappings via Kirk's iterative algorithm in Banach spaces","authors":"Woraphak Nithiarayaphaks, W. Sintunavarat","doi":"10.37193/cjm.2023.02.07","DOIUrl":"https://doi.org/10.37193/cjm.2023.02.07","url":null,"abstract":"Recently Berinde and Păcurar [Approximating fixed points of enriched contractions in Banach spaces. {em J. Fixed Point Theory Appl.} {bf 22} (2020), no. 2., 1--10], first introduced the idea of enriched contraction mappings and proved the existence of a fixed point of an enriched contraction mapping using the well-known fact that any fixed point of {the averaged mapping $T_lambda$, where $lambdain (0,1]$, is also a fixed point of the initial mapping $T$}. In this work, we introduce the idea of weak enriched contraction mappings, and a new generalization of an averaged mapping called double averaged mapping. The first attempt is to prove the existence and uniqueness of the fixed point of a double averaged mapping associated with a weak enriched contraction mapping. Based on this result on Banach spaces, we give some sufficient conditions for the equality of all fixed points of a double averaged mapping and the set {of all fixed points of a weak enriched contraction mapping.} Moreover, our results show that an appropriate Kirk's iterative algorithm can be used to approximate a fixed point of a weak enriched contraction mapping. An illustrative example for showing the efficiency of our results is given.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43089038","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 first introduce the intermixed algorithm in $p$-uniformly convex metric spaces, and then we prove $Delta$-convergence of the proposed iterative method for finding a common element of the sets of fixed points of finite families of nonexpansive mappings in the framework of complete $p$-uniformly convex metric spaces. Furthermore, we apply our main theorem to prove $Delta$-convergence to solve the minimization problems in the framework of complete $p$-uniformly convex metric spaces. Finally, we give two examples in $L^p$ spaces and numerical examples to support our main results.
{"title":"Convergence theorem for an intermixed iteration in $p$-uniformly convex metric space","authors":"Kanyanee Saechou, A. Kangtunyakarn","doi":"10.37193/cjm.2023.02.09","DOIUrl":"https://doi.org/10.37193/cjm.2023.02.09","url":null,"abstract":"In this paper, we first introduce the intermixed algorithm in $p$-uniformly convex metric spaces, and then we prove $Delta$-convergence of the proposed iterative method for finding a common element of the sets of fixed points of finite families of nonexpansive mappings in the framework of complete $p$-uniformly convex metric spaces. Furthermore, we apply our main theorem to prove $Delta$-convergence to solve the minimization problems in the framework of complete $p$-uniformly convex metric spaces. Finally, we give two examples in $L^p$ spaces and numerical examples to support our main results.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41477709","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 research considers Duffing equations with two-component Poisson stable coefficients and excitation. The existence and uniqueness of the Poisson stable solutions have been proved. A new technique for verification of the stability is developed. Numerical simulations of the coefficients, excitation as well as solution are provided.
{"title":"Duffing equations with two-component Poisson stable coefficients","authors":"M. Akhmet, M. Tleubergenova, Akylbek Zhamanshin","doi":"10.37193/cjm.2023.02.01","DOIUrl":"https://doi.org/10.37193/cjm.2023.02.01","url":null,"abstract":"The research considers Duffing equations with two-component Poisson stable coefficients and excitation. The existence and uniqueness of the Poisson stable solutions have been proved. A new technique for verification of the stability is developed. Numerical simulations of the coefficients, excitation as well as solution are provided.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48114388","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}
Autcha Araveeporn, Araya Kheawborisut, A. Kangtunyakarn
In this article, we introduce $G$-subgradient extragradient method for solving the $G$- variational inequality problem in Hilbert space endowed with a direct graph. Utilizing our mathematical tools, weak and strong convergence theorem are established for the proposed algorithm. In addition, we provide numerical experiments to illustrate the convergence behavior of our proposed algorithm.
{"title":"Approximating $G$-variational inequality problem by $G$-subgradient extragradient method in Hilbert space endowed with graphs","authors":"Autcha Araveeporn, Araya Kheawborisut, A. Kangtunyakarn","doi":"10.37193/cjm.2023.02.02","DOIUrl":"https://doi.org/10.37193/cjm.2023.02.02","url":null,"abstract":"In this article, we introduce $G$-subgradient extragradient method for solving the $G$- variational inequality problem in Hilbert space endowed with a direct graph. Utilizing our mathematical tools, weak and strong convergence theorem are established for the proposed algorithm. In addition, we provide numerical experiments to illustrate the convergence behavior of our proposed algorithm.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43581473","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 some existence and stability results for cyclic graphical contractions in complete metric spaces are given. An application to a coupled fixed point problem is also derived."
本文给出了完备度量空间中循环图收缩的一些存在性和稳定性的结果，并给出了在耦合不动点问题中的应用
{"title":"Fixed points and coupled fixed points in $b$-metric spaces via graphical contractions","authors":"Monica-Felicia Bota, L. Guran, G. Petruşel","doi":"10.37193/cjm.2023.01.05","DOIUrl":"https://doi.org/10.37193/cjm.2023.01.05","url":null,"abstract":"\"In this paper some existence and stability results for cyclic graphical contractions in complete metric spaces are given. An application to a coupled fixed point problem is also derived.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41699876","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 introduce the simultaneous and semi-alternating projection algorithms for solving the split equality problem by using a new choice of the step size and combining the alternated inertial technique. The weak convergence of the proposed algorithms is analyzed under standard conditions. Finally, a numerical example is presented to illustrate the efficiency and advantage of the proposed algorithms by comparing with other methods.
{"title":"Alternated inertial simultaneous and semi-alternating projection algorithms for solving the split equality problem","authors":"Q. Dong, Yu Peng","doi":"10.37193/cjm.2023.01.09","DOIUrl":"https://doi.org/10.37193/cjm.2023.01.09","url":null,"abstract":"In this paper, we introduce the simultaneous and semi-alternating projection algorithms for solving the split equality problem by using a new choice of the step size and combining the alternated inertial technique. The weak convergence of the proposed algorithms is analyzed under standard conditions. Finally, a numerical example is presented to illustrate the efficiency and advantage of the proposed algorithms by comparing with other methods.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41759704","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}
T. Mouktonglang, K. Poochinapan, R. Suparatulatorn
In this paper, we construct a new parallel method to solve common variational inclusion and common fixed point problems in a real Hilbert space. We obtain a weak convergence theorem by using this method. Besides, numerical results on the signal recovery problem consisting of various blurred filters present that our proposed method outperforms the two previous methods.
{"title":"A parallel method for common variational inclusion and common fixed point problems with applications","authors":"T. Mouktonglang, K. Poochinapan, R. Suparatulatorn","doi":"10.37193/cjm.2023.01.12","DOIUrl":"https://doi.org/10.37193/cjm.2023.01.12","url":null,"abstract":"In this paper, we construct a new parallel method to solve common variational inclusion and common fixed point problems in a real Hilbert space. We obtain a weak convergence theorem by using this method. Besides, numerical results on the signal recovery problem consisting of various blurred filters present that our proposed method outperforms the two previous methods.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45802608","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}
M. Tleubergenova, Duygu Aruğaslan Çinçin, Zakhira Nugayeva, M. Akhmet
"An unpredictable solution is found for a quasilinear differential equation with generalized piecewise constant argument (EPCAG). Sufficient conditions are provided for the existence, uniqueness and exponential stability of the unpredictable solution. The theoretical results are confirmed by examples and illustrated by simulations."
{"title":"Unpredictable solutions of quasilinear differential equations with generalized piecewise constant arguments of mixed type","authors":"M. Tleubergenova, Duygu Aruğaslan Çinçin, Zakhira Nugayeva, M. Akhmet","doi":"10.37193/cjm.2023.01.18","DOIUrl":"https://doi.org/10.37193/cjm.2023.01.18","url":null,"abstract":"\"An unpredictable solution is found for a quasilinear differential equation with generalized piecewise constant argument (EPCAG). Sufficient conditions are provided for the existence, uniqueness and exponential stability of the unpredictable solution. The theoretical results are confirmed by examples and illustrated by simulations.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44159277","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 look at Diophantine triples with values in three different binary recurrence sequences. These are the Fibonacci and Pell sequences and the sequence of one more of powers of a given prime $p$. The novelty of the article is the appearance of three different sequences, as up to now the analogous problem had been investigated only for one sequence.
{"title":"Diophantine triples with distinct binary recurrences","authors":"F. Luca, L. Szalay","doi":"10.37193/cjm.2023.01.17","DOIUrl":"https://doi.org/10.37193/cjm.2023.01.17","url":null,"abstract":"In this paper, we look at Diophantine triples with values in three different binary recurrence sequences. These are the Fibonacci and Pell sequences and the sequence of one more of powers of a given prime $p$. The novelty of the article is the appearance of three different sequences, as up to now the analogous problem had been investigated only for one sequence.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48131335","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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