MỘT SỐ ĐỊNH LÝ ĐIỂM BẤT ĐỘNG TRONG KHÔNG GIAN E_b-METRIC NÓN
Nội dung chính của bài viết
Tóm tắt
Trong bài báo này, chúng tôi thiết lập điều kiện đủ để một dãy trong không gian -metric nón với những nón chứa các điểm bán trong là -Cauchy. Kết quả này mở rộng và tổng quát hóa các kết quả trong Djedid và cộng sự (2025), Miculescu & Mihail (2017) và Zahia và cộng sự (2023). Chúng tôi cũng suy ra một số định lý điểm cố định trong không gian -metric nón. Những kết quả này là sự tổng quát hóa của một số kết quả đã biết.
Từ khóa
Không gian E_b-metric nón, điểm bất động, điểm bán trong.
Chi tiết bài viết
Tài liệu tham khảo
Al-Rawashdeh, A., Shatanawi, W. & Khandaqji, M. (2012). Normed ordered and E-metric spaces, International Journal of Mathematics and Mathematical Sciences, 2012, 1-11, doi:10.1155/2012/272137.
Basile, A., Graziano, M. G., Papadaki, M. & Polyrakis, I. A. (2017). Cones with semi-interior points and equilibrium. Journal of Mathematical Economics, 71(2017), 36-48, http://dx.doi.org/10.1016/j.jmateco.2017.03.002.
Boriceanu, M. (2009). Fixed point theory on spaces with vector-valued b-metrics. Demonstratio Mathematica, 42(4), 825-836.
Djedid, Z., Al-Sharif, S., Al-Khaleel, M. & Jawdat J. (2023). On solutions of differential and integral equations using new fixed point results in cone E_b-metric spaces. Partial Differential Equations in Applied Mathematics, 8(2023), 1-7, https://doi.org/10.1016/j.padiff.2023.100559.
Djedid, Z., Batiha, I. M., Alsharif, S., Abu-Ghurra, S., Aljazzazi, M. & Jawdat, J. (2025). Fixed point of Hardy-Rogers contraction mappings in non-solid cone χ_b-metric space with applications. Advances in Fxed Point Theory, 15(25), 1-24, https://doi.org/10.28919/afpt/9304.
Du, W. S. (2010). A note on cone metric fixed point theory and its equivalence. Nonlinear Analysis, 72(5), 2259-2261, doi:10.1016/j.na.2009.10.026.
Huang, H. (2019). Topological properties of E-metric spaces with applications to fixed point theory. Mathematics, 7(2019), 1-14, doi:10.3390/math7121222.
Huang, H. & Radenovic, S. (2016). Some fixed point results of generalized Lipschitz mappings on cone b-metric spaces over Banach algebras. Journal of Computational Analysis and Applications, 20(3), 566-583.
Huang, H. & Xu, S. (2013). Fixed point theorems of contractive mappings in cone b-metric spaces and applications. Fixed Point Theory and Applications, 2013(1), 1-10.
Hussain, N. & Shah, M. H. (2011). KKM mappings in cone b-metric spaces. Computers and Mathematics with Applications, 62(4), 1677-1684, doi:10.1016/j.camwa.2011.06.004.
Long-Guang, H. & Xian, Z. (2007). Cone metric spaces and fixed point theorems of contractive mappings. Journal of Mathematical Analysis and Applications, 332(2), 1468-1476, doi:10.1016/j.jmaa.2005.03.087.
Lu, N., He, F. & Du, W. S. (2021). On the best areas for Kannan system and Chatterjea system in b-metric spaces. Optimization, 70(5-6), 973-986, https://doi.org/10.1080/02331934.2020.1727902.
Miculescu, R. & Mihail, A. (2017). New fixed point theorems for set-valued contractions in b-metric spaces. Journal of Fixed Point Theory and Applications, 19(2017), 2153-2163.
Nguyen, V. D. & Vo, T. L. H. (2016). On relaxations of contraction constants and Caristi's theorem in b-metric spaces. Journal of Fixed Point Theory and Applications, 18(2016), 267-284, DOI 10.1007/s11784-015-0273-9.
Rzepecki, B. (1980). On fixed point theorems of Maia type. Publications de l'Institut Mathématique, 28(42), 179-186.
Xu, S., Han, Y., Aleksic, S. & Radenovic, S. (2022). Fixed point results for nonlinear contractions of Perov type in abstract metric spaces with applications. AIMS Mathematics, 7(8), DOI: 10.3934/math.2022817.
Basile, A., Graziano, M. G., Papadaki, M. & Polyrakis, I. A. (2017). Cones with semi-interior points and equilibrium. Journal of Mathematical Economics, 71(2017), 36-48, http://dx.doi.org/10.1016/j.jmateco.2017.03.002.
Boriceanu, M. (2009). Fixed point theory on spaces with vector-valued b-metrics. Demonstratio Mathematica, 42(4), 825-836.
Djedid, Z., Al-Sharif, S., Al-Khaleel, M. & Jawdat J. (2023). On solutions of differential and integral equations using new fixed point results in cone E_b-metric spaces. Partial Differential Equations in Applied Mathematics, 8(2023), 1-7, https://doi.org/10.1016/j.padiff.2023.100559.
Djedid, Z., Batiha, I. M., Alsharif, S., Abu-Ghurra, S., Aljazzazi, M. & Jawdat, J. (2025). Fixed point of Hardy-Rogers contraction mappings in non-solid cone χ_b-metric space with applications. Advances in Fxed Point Theory, 15(25), 1-24, https://doi.org/10.28919/afpt/9304.
Du, W. S. (2010). A note on cone metric fixed point theory and its equivalence. Nonlinear Analysis, 72(5), 2259-2261, doi:10.1016/j.na.2009.10.026.
Huang, H. (2019). Topological properties of E-metric spaces with applications to fixed point theory. Mathematics, 7(2019), 1-14, doi:10.3390/math7121222.
Huang, H. & Radenovic, S. (2016). Some fixed point results of generalized Lipschitz mappings on cone b-metric spaces over Banach algebras. Journal of Computational Analysis and Applications, 20(3), 566-583.
Huang, H. & Xu, S. (2013). Fixed point theorems of contractive mappings in cone b-metric spaces and applications. Fixed Point Theory and Applications, 2013(1), 1-10.
Hussain, N. & Shah, M. H. (2011). KKM mappings in cone b-metric spaces. Computers and Mathematics with Applications, 62(4), 1677-1684, doi:10.1016/j.camwa.2011.06.004.
Long-Guang, H. & Xian, Z. (2007). Cone metric spaces and fixed point theorems of contractive mappings. Journal of Mathematical Analysis and Applications, 332(2), 1468-1476, doi:10.1016/j.jmaa.2005.03.087.
Lu, N., He, F. & Du, W. S. (2021). On the best areas for Kannan system and Chatterjea system in b-metric spaces. Optimization, 70(5-6), 973-986, https://doi.org/10.1080/02331934.2020.1727902.
Miculescu, R. & Mihail, A. (2017). New fixed point theorems for set-valued contractions in b-metric spaces. Journal of Fixed Point Theory and Applications, 19(2017), 2153-2163.
Nguyen, V. D. & Vo, T. L. H. (2016). On relaxations of contraction constants and Caristi's theorem in b-metric spaces. Journal of Fixed Point Theory and Applications, 18(2016), 267-284, DOI 10.1007/s11784-015-0273-9.
Rzepecki, B. (1980). On fixed point theorems of Maia type. Publications de l'Institut Mathématique, 28(42), 179-186.
Xu, S., Han, Y., Aleksic, S. & Radenovic, S. (2022). Fixed point results for nonlinear contractions of Perov type in abstract metric spaces with applications. AIMS Mathematics, 7(8), DOI: 10.3934/math.2022817.