On D_b-metric and general partial b-metric spaces
DOI:
https://doi.org/10.29304/jqcm.2020.12.2.698Keywords:
b-metric, partial b-metric, D-metric, D_b-metric and general partial b-metric spacesAbstract
In this paper, we introduce a new type of generalize metric space, which we call -metric space as a generalization of both -metric and b-metric spaces. Then we prove some fixed point theorem in this space. Also we define a general partial b-metric space as a generalize of a partial b-metric space and study their properties. Finally, find relation between partial b-metric, -metric and general partial b-metric spaces.
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References
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[2] CZERWIK, Stefan. Contraction mappings in $ b $-metric spaces. Acta mathematica et informatica universitatis ostraviensis, 1993, 1.1: 5-11.
[3] ALQAHTANI, Badr; FULGA, Andreea; KARAPINAR, Erdal. Non-unique fixed point results in extended b-metric space. Mathematics, 2018, 6.5: 68.
[4] CHIFU, Cristian, et al. FIXED POINTS FOR MULTIVALUED CONTRACTIONS IN $ b $-METRIC SPACES WITH APPLICATIONS TO FRACTALS. Taiwanese Journal of Mathematics, 2014, 18.5: 1365-1375.
[5] KUMARI, Sudesh, et al. Multi fractals of generalized multivalued iterated function systems in b-metric spaces with applications. Mathematics, 2019, 7.10: 967.
[6] Dhage, B. C. Generalized metric spaces and topological structure. I, Analele Atintifice ale Universitatii Al. I. Cuza din lasi. Serie Noua Mathematica. 2000, 46,3, 24.
[7] FORA, Ali Ahmad Ali; MASSA'DEH, Mourad Oqla; BATAINEH, Mohammad Saleh. A New Structure and Contribution in D-metric Spaces. Journal of Advances in Mathematics and Computer Science, 2017, 1-9.
[8] Ramabhadrasarma, I.; SambasIvarao, S. ON D-METRIC SPACES, Journal of Global Research in Mathematical Archives. 2013, 1,12.
[9] RHOADES, B. E. A fixed point theorem for generalized metric spaces. International Journal of Mathematics and Mathematical Sciences, 1996, 19.3: 457-460.
[10] SHUKLA, Satish. Partial b-metric spaces and fixed point theorems. Mediterranean Journal of Mathematics, 2014, 11.2: 703-711.
[11] AMEER, Eskandar, et al. Hybrid multivalued type contraction mappings in αK-complete partial b-metric spaces and applications. Symmetry, 2019, 11.1: 86.
[2] VAN DUNG, Nguyen; LE HANG, Vo Thi. Remarks on partial b-metric spaces and fixed point theorems. Matematicki Vesnik, 2017, 69.4: 231-240.
[13] MUSTAFA, Zead, et al. Some common fixed point results in ordered partial b-metric spaces. Journal of Inequalities and Applications, 2013, 2013.1: 562.
[2] CZERWIK, Stefan. Contraction mappings in $ b $-metric spaces. Acta mathematica et informatica universitatis ostraviensis, 1993, 1.1: 5-11.
[3] ALQAHTANI, Badr; FULGA, Andreea; KARAPINAR, Erdal. Non-unique fixed point results in extended b-metric space. Mathematics, 2018, 6.5: 68.
[4] CHIFU, Cristian, et al. FIXED POINTS FOR MULTIVALUED CONTRACTIONS IN $ b $-METRIC SPACES WITH APPLICATIONS TO FRACTALS. Taiwanese Journal of Mathematics, 2014, 18.5: 1365-1375.
[5] KUMARI, Sudesh, et al. Multi fractals of generalized multivalued iterated function systems in b-metric spaces with applications. Mathematics, 2019, 7.10: 967.
[6] Dhage, B. C. Generalized metric spaces and topological structure. I, Analele Atintifice ale Universitatii Al. I. Cuza din lasi. Serie Noua Mathematica. 2000, 46,3, 24.
[7] FORA, Ali Ahmad Ali; MASSA'DEH, Mourad Oqla; BATAINEH, Mohammad Saleh. A New Structure and Contribution in D-metric Spaces. Journal of Advances in Mathematics and Computer Science, 2017, 1-9.
[8] Ramabhadrasarma, I.; SambasIvarao, S. ON D-METRIC SPACES, Journal of Global Research in Mathematical Archives. 2013, 1,12.
[9] RHOADES, B. E. A fixed point theorem for generalized metric spaces. International Journal of Mathematics and Mathematical Sciences, 1996, 19.3: 457-460.
[10] SHUKLA, Satish. Partial b-metric spaces and fixed point theorems. Mediterranean Journal of Mathematics, 2014, 11.2: 703-711.
[11] AMEER, Eskandar, et al. Hybrid multivalued type contraction mappings in αK-complete partial b-metric spaces and applications. Symmetry, 2019, 11.1: 86.
[2] VAN DUNG, Nguyen; LE HANG, Vo Thi. Remarks on partial b-metric spaces and fixed point theorems. Matematicki Vesnik, 2017, 69.4: 231-240.
[13] MUSTAFA, Zead, et al. Some common fixed point results in ordered partial b-metric spaces. Journal of Inequalities and Applications, 2013, 2013.1: 562.
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Published
2020-07-10
How to Cite
Abdullah, N. I., & Shaakir, L. K. (2020). On D_b-metric and general partial b-metric spaces. Journal of Al-Qadisiyah for Computer Science and Mathematics, 12(2), Math Page 74– 86. https://doi.org/10.29304/jqcm.2020.12.2.698
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Math Articles
