In this paper, we introduce two new classes of nonlinear mappings and present some new existence and convergence theorems for these mappings in Banach spaces. More precisely, we employ the Krasnosel'skii iterative method to obtain fixed points of Suzuki-enriched nonexpansive mappings under different conditions. Moreover, we approximate the fixed point of enriched-quasinonexpansive mappings via Ishikawa iterative method.
{"title":"Some fixed point results for enriched nonexpansive type mappings in Banach spaces","authors":"Rahul Shukla, R. Pant","doi":"10.4995/agt.2022.16165","DOIUrl":"https://doi.org/10.4995/agt.2022.16165","url":null,"abstract":"In this paper, we introduce two new classes of nonlinear mappings and present some new existence and convergence theorems for these mappings in Banach spaces. More precisely, we employ the Krasnosel'skii iterative method to obtain fixed points of Suzuki-enriched nonexpansive mappings under different conditions. Moreover, we approximate the fixed point of enriched-quasinonexpansive mappings via Ishikawa iterative method. ","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"5 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78616082","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}
In this paper, selection principles are defined and studied in the realm of irresolute topological groups. Especially, s-Menger-bounded and s-Rothberger-bounded type covering properties are introduced and studied.
{"title":"Selection principles: s-Menger and s-Rothberger-bounded groups","authors":"M. A. Iqbal, M. Khan","doi":"10.4995/agt.2022.14846","DOIUrl":"https://doi.org/10.4995/agt.2022.14846","url":null,"abstract":"In this paper, selection principles are defined and studied in the realm of irresolute topological groups. Especially, s-Menger-bounded and s-Rothberger-bounded type covering properties are introduced and studied.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"6 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80566153","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}
In this paper, we present some results on fixed point index calculations for multivalued mappings and apply them to prove the existence of solutions to multivalued equations in ordered space, under flexible conditions for the positive eigenvalue.
{"title":"Fixed point index computations for multivalued mapping and application to the problem of positive eigenvalues in ordered space","authors":"Vo Viet Tri","doi":"10.4995/agt.2022.15669","DOIUrl":"https://doi.org/10.4995/agt.2022.15669","url":null,"abstract":"In this paper, we present some results on fixed point index calculations for multivalued mappings and apply them to prove the existence of solutions to multivalued equations in ordered space, under flexible conditions for the positive eigenvalue.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"19 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83013273","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}
Bornologies abstract the properties of bounded sets of a metric space. But there are unbounded bornologies on a metric space like $mathcal{P}(RR)$ with the Euclidean metric. We show that by replacing $[0,infty)$ with a partially ordered monoid every bornology is the set of bounded subsets of a generalized metric mapped into a partially ordered monoid. We also prove that the set of bornologies on a set is the join completion of the equivalence classes of a relation on the power set of the set.
{"title":"Representations of bornologies","authors":"H. Pajoohesh","doi":"10.4995/agt.2022.16405","DOIUrl":"https://doi.org/10.4995/agt.2022.16405","url":null,"abstract":"Bornologies abstract the properties of bounded sets of a metric space. But there are unbounded bornologies on a metric space like $mathcal{P}(RR)$ with the Euclidean metric. We show that by replacing $[0,infty)$ with a partially ordered monoid every bornology is the set of bounded subsets of a generalized metric mapped into a partially ordered monoid. We also prove that the set of bornologies on a set is the join completion of the equivalence classes of a relation on the power set of the set.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"9 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76339129","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}
In this paper, we introduce the notion order quasi-Cauchy se-quences, downward and upward order quasi-cauchy sequences, order half Cauchy sequences. Next we consider associated idea of continuity namely, ward order continuous functions [2] and investigated certain intersting results. The entire investigation is perform in (l)-group setting.
{"title":"On certain new notion of order Cauchy sequences, continuity in (l)-group","authors":"S. Pal, S. Chakraborty","doi":"10.4995/agt.2022.16126","DOIUrl":"https://doi.org/10.4995/agt.2022.16126","url":null,"abstract":"In this paper, we introduce the notion order quasi-Cauchy se-quences, downward and upward order quasi-cauchy sequences, order half Cauchy sequences. Next we consider associated idea of continuity namely, ward order continuous functions [2] and investigated certain intersting results. The entire investigation is perform in (l)-group setting.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"26 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86955553","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}
In this paper, we introduce a new concept of KW-type ω-contraction mixed multivalued mapping. After that, we obtain some fixed point results for both multivalued and single valued mappings Finally, we provide a noteworth example to show the effectiveness of our result.
{"title":"Some generalizations for mixed multivalued mappings","authors":"M. Aslantaş, H. Sahin, Uğur Sadullah","doi":"10.4995/agt.2022.15214","DOIUrl":"https://doi.org/10.4995/agt.2022.15214","url":null,"abstract":"In this paper, we introduce a new concept of KW-type ω-contraction mixed multivalued mapping. After that, we obtain some fixed point results for both multivalued and single valued mappings Finally, we provide a noteworth example to show the effectiveness of our result.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"64 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78207897","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}
Since Hochster's work, spectral spaces have attracted increasing interest. Through this note we give a new self-contained and constructible topology-independent proof of the fact that the set of proper ideals of a ring endowed with coarse lower topology is a spectral space.
{"title":"Proper spaces are spectral","authors":"A. Goswami","doi":"10.4995/agt.2023.17800","DOIUrl":"https://doi.org/10.4995/agt.2023.17800","url":null,"abstract":"Since Hochster's work, spectral spaces have attracted increasing interest. Through this note we give a new self-contained and constructible topology-independent proof of the fact that the set of proper ideals of a ring endowed with coarse lower topology is a spectral space.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"144 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73499338","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}
In this paper, we aim to revisit some non-unique fixed point theorems that were initiated by Ćirić, first.We consider also some natural consequences of the obtained results. In addition, we provide a simple example to illustrate the validity of the main result.
{"title":"Revisiting Ciric type nonunique fixed point theorems via interpolation","authors":"E. Karapınar","doi":"10.4995/agt.2021.16562","DOIUrl":"https://doi.org/10.4995/agt.2021.16562","url":null,"abstract":"In this paper, we aim to revisit some non-unique fixed point theorems that were initiated by Ćirić, first.We consider also some natural consequences of the obtained results. In addition, we provide a simple example to illustrate the validity of the main result.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"49 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81407145","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}
As in [6, 3, 4, 5], we discuss published assertions concerning fixed points in “digital metric spaces” - assertions that are incorrect or incorrectly proven, or reduce to triviality.
{"title":"Remarks on fixed point assertions in digital topology, 5","authors":"L. Boxer","doi":"10.4995/agt.2022.16655","DOIUrl":"https://doi.org/10.4995/agt.2022.16655","url":null,"abstract":"As in [6, 3, 4, 5], we discuss published assertions concerning fixed points in “digital metric spaces” - assertions that are incorrect or incorrectly proven, or reduce to triviality.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"81 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74973494","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}
Let R be a commutative ring with identity and M a unitary R-module. The primary-like spectrum SpecL(M) is the collection of all primary-like submodules Q of M, the recent generalization of primary ideals, such that M/Q is a primeful R-module. In this article, we topologies SpecL(M) with the patch-like topology, and show that when, SpecL(M) with the patch-like topology is a quasi-compact, Hausdorff, totally disconnected space.
{"title":"A new topology over the primary-like spectrum of a module","authors":"F. Rashedi","doi":"10.4995/agt.2021.13225","DOIUrl":"https://doi.org/10.4995/agt.2021.13225","url":null,"abstract":"Let R be a commutative ring with identity and M a unitary R-module. The primary-like spectrum SpecL(M) is the collection of all primary-like submodules Q of M, the recent generalization of primary ideals, such that M/Q is a primeful R-module. In this article, we topologies SpecL(M) with the patch-like topology, and show that when, SpecL(M) with the patch-like topology is a quasi-compact, Hausdorff, totally disconnected space.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"3 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89921953","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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