Article Sidebar
Date Published:
16/04/2015
Online Published:
15/04/2015
Abstract Views: 203
Views PDF: 64
Views PDF: 64
Section
Natural Sciences Issue (Vietnamese)
How to Cite
Nguyen, T. H. (2015). Fixed point theorems for contractions of rational type in ordered rectangular metric spaces. Dong Thap University Journal of Science, 12, 81-87. https://doi.org/10.52714/dthu.12.4.2015.188
Citation format:
Metrics
Fixed point theorems for contractions of rational type in ordered rectangular metric spaces
Main Article Content
Abstract
In this paper, we establish and prove some fixed point theorems for the contraction of rational type in ordered rectangular metric spaces. The obtained results are the generalizations of those in [4, 8]. Also, relevant examples are provided for illustration.
Keywords
Fixed point, the contraction of rational type, ordered rectangular metric space.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
References
[1]. H. Aydi, E. Karapinar, and H. Lakzian (2012), “Fixed point results on a class of generalized metric spaces”, Math. Sci., 6:46, 6 pages.
[2]. H. Aydi, E. Karapinar, and B. Samet (2014), “Fixed points for generalized -contractions on generalized metric spaces”, J. Inequal. Appl., 2014:229, 16 pages.
[3]. A. Branciari (2000), “A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces”, Publ. Math. Debrecen, 57, pp.31- 37.
[4]. N. V. Can and N. X. Thuan (2013), “Fixed point theorem for generalized weak contractions involving rational expressions”, Open J. Math. Modeling, 1(2), pp.29-33.
[5]. S. Chandok, B. S. Choudhury, and N. Metiya (2014), “Fixed point results in ordered metric spaces for rational type expressions with auxiliary functions”, J. Egyptian Math. Soc., 7 pages, in press.
[6]. I. Cabrera, J. Harjani, and K. Sadarangani (2013), “A fixed point theorem for contractions of rational type in partially ordered metric spaces”, Ann. Univ. Ferrara, 59, 251-258.
[7]. B. K. Dass and S. Gupta (1975), “A extension of Banach contraction principle through rational expression”, Indian J. Pure Appl. Math., 6 (12), 1455-1458.
[8]. I. M Erhan, E. Karapinar, and T. Sekulic (2012), “Fixed points of contractions on rectangular metric spaces”, Fixed Point Theory Appl., 2012:138, 12 pages
[9]. W. Kirk and N. Shahzad (2013), “Generalized metrics and Caristi’s theorem”, Fixed Point Theory Appl., 2013:129, 9 pages.
[10]. R. P. Pathak, R. Tiwari, and R. Bhardwaj (2014), “Fixed point theorems through rational expression in altering distance functions”, Math. Theory Modeling, 4 (7), pp.78- 83.
[2]. H. Aydi, E. Karapinar, and B. Samet (2014), “Fixed points for generalized -contractions on generalized metric spaces”, J. Inequal. Appl., 2014:229, 16 pages.
[3]. A. Branciari (2000), “A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces”, Publ. Math. Debrecen, 57, pp.31- 37.
[4]. N. V. Can and N. X. Thuan (2013), “Fixed point theorem for generalized weak contractions involving rational expressions”, Open J. Math. Modeling, 1(2), pp.29-33.
[5]. S. Chandok, B. S. Choudhury, and N. Metiya (2014), “Fixed point results in ordered metric spaces for rational type expressions with auxiliary functions”, J. Egyptian Math. Soc., 7 pages, in press.
[6]. I. Cabrera, J. Harjani, and K. Sadarangani (2013), “A fixed point theorem for contractions of rational type in partially ordered metric spaces”, Ann. Univ. Ferrara, 59, 251-258.
[7]. B. K. Dass and S. Gupta (1975), “A extension of Banach contraction principle through rational expression”, Indian J. Pure Appl. Math., 6 (12), 1455-1458.
[8]. I. M Erhan, E. Karapinar, and T. Sekulic (2012), “Fixed points of contractions on rectangular metric spaces”, Fixed Point Theory Appl., 2012:138, 12 pages
[9]. W. Kirk and N. Shahzad (2013), “Generalized metrics and Caristi’s theorem”, Fixed Point Theory Appl., 2013:129, 9 pages.
[10]. R. P. Pathak, R. Tiwari, and R. Bhardwaj (2014), “Fixed point theorems through rational expression in altering distance functions”, Math. Theory Modeling, 4 (7), pp.78- 83.
Most read articles by the same author(s)
- Trung Hieu Nguyen, Quoc Ai Ho, Về định lí điểm bất động cho lớp ánh xạ Meir-Keeler -co trên không gian Kiểu b-mêtric , Dong Thap University Journal of Science: No. 9 (2014): Part B - Natural Sciences
- Kim Ngoan Nguyen, Trung Hieu Nguyen, Convergence of agarwal-type iteration process to common fixed points of two generalized -nonexpansive mappings in uniformly convex Banach spaces , Dong Thap University Journal of Science: No. 37 (2019): Part B - Natural Sciences
- Thi Kieu Ngan Doan, Trung Hieu Nguyen, Some common fixed point theorems for -weak nonlinear contraction in partially ordered metric-type spaces , Dong Thap University Journal of Science: No. 13 (2015): Part B - Natural Sciences
- Trung Hieu Nguyen, Thi Kim Tuyen Nguyen, Designing a teaching scenario for the chapter on fractions to foster 6th-grade students’ mathematical communication competence , Dong Thap University Journal of Science: Vol. 14 No. 06S (2025): Special Issue of Social Sciences and Humanities (Vietnamese)
- Trung Hieu Nguyen, Thi Phuong Thao Le, Designing teaching situations to develop mathematical thinking and reasoning competence in teaching the topic of Equations – Grade 8 Math , Dong Thap University Journal of Science: Vol. 14 No. 07S (2025): Special Issue of Social Sciences and Humanities (Vietnamese)