<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">cheb</journal-id><journal-title-group><journal-title xml:lang="ru">Чебышевский сборник</journal-title><trans-title-group xml:lang="en"><trans-title>Chebyshevskii Sbornik</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2226-8383</issn><publisher><publisher-name>Tula State Lev Tolstoy  Pedagogical University</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.22405/2226-8383-2024-25-1-155-163</article-id><article-id custom-type="elpub" pub-id-type="custom">cheb-1683</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Краткие сообщения</subject></subj-group></article-categories><title-group><article-title>Расстояние 𝑊𝑡− над метрическим пространством 𝑏−</article-title><trans-title-group xml:lang="en"><trans-title>𝑊𝑡− Distance over 𝑏− Metric Space</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Альмухур</surname><given-names>Эман</given-names></name><name name-style="western" xml:lang="en"><surname>Almukhur</surname><given-names>Eman</given-names></name></name-alternatives><bio xml:lang="ru"><p>факультет фундаментальных и гуманитарных наук</p></bio><bio xml:lang="en"><p>department of basic science and humanities</p></bio><email xlink:type="simple">e_almuhur@asu.edu.jo</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Кусини</surname><given-names>Майсун</given-names></name><name name-style="western" xml:lang="en"><surname>Qousini</surname><given-names>Maysoon</given-names></name></name-alternatives><bio xml:lang="ru"><p>кафедра математики</p></bio><bio xml:lang="en"><p>department of mathematics</p></bio><email xlink:type="simple">M.qousini@zuj.edu.jo</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Альнана</surname><given-names>Абир</given-names></name><name name-style="western" xml:lang="en"><surname>Alnana</surname><given-names>Abeer</given-names></name></name-alternatives><bio xml:lang="ru"><p>факультет математики</p></bio><bio xml:lang="en"><p>department of mathematics</p></bio><email xlink:type="simple">a.alnana@psau.edu.sa</email><xref ref-type="aff" rid="aff-3"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Аль-Лабади</surname><given-names>Манал</given-names></name><name name-style="western" xml:lang="en"><surname>Al-Labadi</surname><given-names>Manal</given-names></name></name-alternatives><bio xml:lang="ru"><p>кафедра математики</p></bio><bio xml:lang="en"><p>department of mathematics</p></bio><email xlink:type="simple">Manal.allabadi@uop.edu.jo</email><xref ref-type="aff" rid="aff-4"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Частный университет прикладных наук (г. Амман, Иордания).</institution><country>Иордания</country></aff><aff xml:lang="en"><institution>Applied Science Private University (Amman, Jordan).</institution><country>Jordan</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Иорданский университет Аль-Зайтуна (г. Амман, Иордания).</institution><country>Иордания</country></aff><aff xml:lang="en"><institution>Al-Zaytoonah University of Jordan (Amman, Jordan).</institution><country>Jordan</country></aff></aff-alternatives><aff-alternatives id="aff-3"><aff xml:lang="ru"><institution>Университет принца Саттама бин Абдулазиза (г. Аль-Хардж, Саудовская Аравия).</institution><country>Саудовская Аравия</country></aff><aff xml:lang="en"><institution>Prince Sattam Bin Abdulaziz University (Al-Kharj, Saudi Arabia).</institution><country>Saudi Arabia</country></aff></aff-alternatives><aff-alternatives id="aff-4"><aff xml:lang="ru"><institution>Университет Петры (г. Амман, Иордания).</institution><country>Иордания</country></aff><aff xml:lang="en"><institution>University Of Petra (Amman, Jordan).</institution><country>Jordan</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>24</day><month>04</month><year>2024</year></pub-date><volume>25</volume><issue>1</issue><fpage>155</fpage><lpage>163</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Альмухур Э., Кусини М., Альнана А., Аль-Лабади М., 2024</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="ru">Альмухур Э., Кусини М., Альнана А., Аль-Лабади М.</copyright-holder><copyright-holder xml:lang="en">Almukhur E., Qousini M., Alnana A., Al-Labadi M.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://www.chebsbornik.ru/jour/article/view/1683">https://www.chebsbornik.ru/jour/article/view/1683</self-uri><abstract><p>В этой работе мы исследуем характеристики 𝑤𝑡−расстояния характеристики над 𝑏−метрическим пространством и условия, необходимые для обеспечения наличие неподвижной точки, если позволить 𝛽−функции соответствующим образом. Кроме того, мыдоказываем некоторые теоремы о неподвижной точке.</p></abstract><trans-abstract xml:lang="en"><p>In this paper, we examine the 𝑤𝑡−distance characteristics over 𝑏−metric space and the conditions required to ensure the presence of the fixed point by letting 𝛽−function appropriately.In addition, we prove some fixed point theorems.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>𝑤𝑡− метрика</kwd><kwd>𝑏− метрика</kwd><kwd>𝛽− функция</kwd><kwd>неподвижная точка.</kwd></kwd-group><kwd-group xml:lang="en"><kwd>𝑤𝑡− metric</kwd><kwd>𝑏− metric</kwd><kwd>𝛽− function</kwd><kwd>fixed point.</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Czerwik S. Nonlinear set-valued contraction mappings in 𝑏− metric spaces // Atti del Seminario Matematico e Fisico dell’Universita di Modena, 46, (1998), 263–276.</mixed-citation><mixed-citation xml:lang="en">Czerwik S. 1998, “Nonlinear set-valued contraction mappings in 𝑏−metric spaces”, Atti del Seminario Matematico e Fisico dell’Universita di Modena, 46, pp. 263–276.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Bakhtin I.A. The contraction mapping principle in quasimetric spaces // Journal of Functional Analysis, 1989, 30, pp. 26–37.</mixed-citation><mixed-citation xml:lang="en">Bakhtin, I.A., 1989. “The contraction mapping principle in quasimetric spaces”, Journal of Functional Analysis, 30, pp. 26–37.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Gromov M. Groups of polynomial growth and expanding maps // Publications Math´ematiques de l’Institut des Hautes ´Etudes Scientifiques. 53, 1981, pp. 53–73.</mixed-citation><mixed-citation xml:lang="en">Gromov M.,1981. “Groups of polynomial growth and expanding maps”, Publications Math´ematiques de l’Institut des Hautes ´ Etudes Scientifiques, 53: pp. 53–73.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">doi:10.1007/BF02698687. MR 0623534. S2CID 121512559. Zbl 0474.20018.</mixed-citation><mixed-citation xml:lang="en">doi:10.1007/BF02698687. MR 0623534. S2CID 121512559. Zbl 0474.20018.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Kurepa, D.J. Tableaux ramifi´es d’ensembles, espaces pseudodistaci´es // Comptes Rendus de l’Acad´emie des Sciences . Paris. 198, 1934, pp. 1563–1565.</mixed-citation><mixed-citation xml:lang="en">Kurepa, D.J., 1934. “Tableaux ramifi´es d’ensembles, espaces pseudodistaci´es”, Comptes Rendus de l’Acad´emie des Sciences . Paris, 198, pp. 1563–1565.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Branciari A. A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces // Publicationes Mathematicae Debrecen, 57, 2000, pp. 31–37. MR1771669.</mixed-citation><mixed-citation xml:lang="en">Branciari A., 2000. “A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces”, Publicationes Mathematicae Debrecen, 57, pp. 31–37. MR1771669.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Suzuki T. Journal of Inequalities and Applications, 256, 2017, pp. 1–11. http://dx.doi.org/10.1186/s13660-017-1528-3.</mixed-citation><mixed-citation xml:lang="en">Suzuki T.,2017. “Journal of Inequalities and Applications”, 256, pp. 1–11. http://dx.doi.org/10.1186/s13660-017-1528-3.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Singh SL, Czerwik S, Kr´ol, K and Singh. A Coincidences and fixed points of hybrid contractions. Tamsui Oxford Journal of Information and Mathematical Sciences. 24, pp. 401-416.</mixed-citation><mixed-citation xml:lang="en">Singh SL, Czerwik S, Kr´ol, K. &amp; Singh, 2008. “A Coincidences and fixed points of hybrid contractions”, Tamsui Oxford Journal of Information and Mathematical Sciences, 24, pp. 401–416.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Rockafellar R, Tyrrell; Wets, Roger J-B. Variational Analysis // Springer-Verlag, 2005, p. 117.</mixed-citation><mixed-citation xml:lang="en">Rockafellar R, Tyrrell; Wets, Roger J-B, 2005. “Variational Analysis”, Springer-Verlag, p. 117.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Berinde, V. Generalized contractions in quasimetric spaces // Semin. Fixed Point Theory, 3, 1993, pp. 3–9.</mixed-citation><mixed-citation xml:lang="en">Berinde, V., 1993. “‘Generalized contractions in quasimetric spaces”, Semin. Fixed Point Theory, 3, pp. 3–9.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Rus, I.A. Generalized Contractions and Applications // Cluj University Press: Clui-Napoca, Romania, 2001.</mixed-citation><mixed-citation xml:lang="en">Rus, I.A.,2001. “Generalized Contractions and Applications”, Cluj University Press: Clui-Napoca, Romania.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Karapınar E, Chifu C. Results in wt-Distance over 𝑏-Metric Spaces // SIGMA Mathematics, 220(8), 2020, pp. 1–10.</mixed-citation><mixed-citation xml:lang="en">Karapınar E, Chifu C., 2020. “Results in 𝑤𝑡-Distance over 𝑏-Metric Spaces”, SIGMA Mathematics, 220(8), pp. 1–10.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Popescu, O. Some new fixed point theorems for 𝛽− Geraghty contractive type maps in metric spaces // Fixed Point Theory and Applications, 190 p. (2014). https://doi.org/10.1186/1687-1812-2014-190.</mixed-citation><mixed-citation xml:lang="en">Popescu, O., 2014. “Some new fixed point theorems for 𝛽−Geraghty contractive type maps in metric spaces”, Fixed Point Theory and Applications, 190 p.. https://doi.org/10.1186/1687-1812-2014-190.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Khojasteh, F.; Shukla, S.; Radenovi C, S. A new approach to the study of fixed point theorems via simulation functions // Filomat, 29, 2015, pp. 1189–1194.</mixed-citation><mixed-citation xml:lang="en">Khojasteh, F., Shukla, S., Radenovi, C. S., 2015. “A new approach to the study of fixed point theorems via simulation functions”, Filomat, 29, pp. 1189–1194.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Aydi, H. Fixed point results for weakly contractive mappings in ordered partial metric spaces // Journal of Advanced Mathematical Studies, 4(2), 2011, pp. 1–12.</mixed-citation><mixed-citation xml:lang="en">Aydi, H.,2011. “Fixed point results for weakly contractive mappings in ordered partial metric spaces”, Journal of Advanced Mathematical Studies, 4(2), pp. 1–12.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Al-Sharif, S., Al-Khaleel, M., Khandaqji, M. Coupled Fixed Point Theorems for Nonlinear Contractions in Partial Metric Spaces // International Journal of Mathematics and Mathematical Sciences, 2012, pp. 1-12.</mixed-citation><mixed-citation xml:lang="en">Al-Sharif, S., Al-Khaleel, M., Khandaqji, M., 2012. “Coupled Fixed Point Theorems for Nonlinear Contractions in Partial Metric Spaces”, International Journal of Mathematics and Mathematical Sciences, pp. 1-12.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
