An affirmative answer to quasi-contraction's open problem under some local constraints in JS-metric spaces
In this work, we first present JS-Pompeiu-Hausdorff metric in JS metric spaces and then introduce well-behaved quasi-contraction in order to find an affirmative answer to quasi-contractions’ open problem under some local constraints in JS-metric spaces. In the literature, this problem solved when th...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2019-06-01
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| Series: | Mathematical Modelling and Analysis |
| Subjects: | |
| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/6495 |
| _version_ | 1818322098513248256 |
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| author | Sanaz Pourrazi Farshid Khojasteh Mojgan Javahernia Hasan Khandani |
| author_facet | Sanaz Pourrazi Farshid Khojasteh Mojgan Javahernia Hasan Khandani |
| author_sort | Sanaz Pourrazi |
| collection | DOAJ |
| description | In this work, we first present JS-Pompeiu-Hausdorff metric in JS metric spaces and then introduce well-behaved quasi-contraction in order to find an affirmative answer to quasi-contractions’ open problem under some local constraints in JS-metric spaces. In the literature, this problem solved when the constant modules α ∈ [0,1/2] and when α ∈ (1/2,1], finding conditions by which the set of all fixed points be non-empty, has remained open yet. Moreover, we support our result by a notable example. Finally, by taking into account the approximate strict fixed point property we present some worthwhile open problems in these spaces. |
| first_indexed | 2024-12-13T10:51:24Z |
| format | Article |
| id | doaj.art-c918442137e1462b9d42ca07cad587bb |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-13T10:51:24Z |
| publishDate | 2019-06-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-c918442137e1462b9d42ca07cad587bb2022-12-21T23:49:48ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102019-06-0124310.3846/mma.2019.027An affirmative answer to quasi-contraction's open problem under some local constraints in JS-metric spacesSanaz Pourrazi0Farshid Khojasteh1Mojgan Javahernia2Hasan Khandani3Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, IranYoung Researcher and Elite Club, Arak Branch, Islamic Azad University, Arak, IranDepartment of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, IranDepartment of Mathematics, Mahabad Branch, Islamic Azad University, Mahabad, IranIn this work, we first present JS-Pompeiu-Hausdorff metric in JS metric spaces and then introduce well-behaved quasi-contraction in order to find an affirmative answer to quasi-contractions’ open problem under some local constraints in JS-metric spaces. In the literature, this problem solved when the constant modules α ∈ [0,1/2] and when α ∈ (1/2,1], finding conditions by which the set of all fixed points be non-empty, has remained open yet. Moreover, we support our result by a notable example. Finally, by taking into account the approximate strict fixed point property we present some worthwhile open problems in these spaces.https://journals.vgtu.lt/index.php/MMA/article/view/6495Iterative fixed pointStrict fixed pointJS-Pompieu HausdorffWell-behaved quasi contraction |
| spellingShingle | Sanaz Pourrazi Farshid Khojasteh Mojgan Javahernia Hasan Khandani An affirmative answer to quasi-contraction's open problem under some local constraints in JS-metric spaces Mathematical Modelling and Analysis Iterative fixed point Strict fixed point JS-Pompieu Hausdorff Well-behaved quasi contraction |
| title | An affirmative answer to quasi-contraction's open problem under some local constraints in JS-metric spaces |
| title_full | An affirmative answer to quasi-contraction's open problem under some local constraints in JS-metric spaces |
| title_fullStr | An affirmative answer to quasi-contraction's open problem under some local constraints in JS-metric spaces |
| title_full_unstemmed | An affirmative answer to quasi-contraction's open problem under some local constraints in JS-metric spaces |
| title_short | An affirmative answer to quasi-contraction's open problem under some local constraints in JS-metric spaces |
| title_sort | affirmative answer to quasi contraction s open problem under some local constraints in js metric spaces |
| topic | Iterative fixed point Strict fixed point JS-Pompieu Hausdorff Well-behaved quasi contraction |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/6495 |
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