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Date Published:
16/04/2015
Online Published:
15/04/2015
Abstract Views: 22
Views PDF: 10
Views PDF: 10
Section
Natural Sciences Issue
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
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.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Keywords
Fixed point, the contraction of rational type, ordered rectangular metric space.
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.
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