پیوندهای مفید
آمار
| تعداد نشریات | 22 |
| تعداد شمارهها | 705 |
| تعداد مقالات | 10,149 |
| تعداد مشاهده مقاله | 71,507,396 |
| تعداد دریافت فایل اصل مقاله | 63,219,313 |
Best proximity point theorem in higher dimensions with an application | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 13، Special Issue for selected papers of ICDACT-2021، خرداد 2022، صفحه 97-108 اصل مقاله (374.69 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.6335 | ||
| نویسندگان | ||
| Saranan Mondal1؛ Supriti Laha1؛ Ankush Chanda* 2 | ||
| 1Department of Mathematics, National Institute of Technology, Durgapur, West Bengal, India | ||
| 2Department of Mathematics, Vellore Institute of Technology, Vellore, India | ||
| تاریخ دریافت: 21 مرداد 1400، تاریخ بازنگری: 29 آذر 1400، تاریخ پذیرش: 22 دی 1400 | ||
| چکیده | ||
| In this article, we introduce the notion of $F_n$-contractions $T:A^n\rightarrow B$ in standard metric spaces and explore the possibility of certain approximation results for these mappings. We prove the existence and uniqueness of $n$-tuple ($n \geq 2$) best proximity points of $F_n$-contractions, not necessarily continuous, using the weak $P$-property in complete metric spaces. Additionally, suitable examples are presented to substantiate our main results. Moreover, we anticipate a fixed point result to prove the existence and uniqueness of the solution for a type of integral equation to elucidate our obtained theorems. | ||
| کلیدواژهها | ||
| $F_n$-contractions؛ best proximity points؛ $P$-property؛ weak $P$-property؛ $n$-tuple best proximity points | ||
| مراجع | ||
|
[1] M. Abbas, W. Sintunavarat and P. Kumam, Coupled fixed point in partially ordered G-metric spaces, Fixed Point Theory Appl. 2012 (2012), 31. [2] V. Berinde and M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011), no. 15, 4889–4897. [3] J. Caballero, J. Harjani and K. Sadarangani, A best proximity point theorem for Geraghty-contractions, Fixed Point Theory Appl. 2012 (2012), 231. [4] P. Das and L.K. Dey, Fixed point of contractive mappings in generalized metric spaces, Math. Slovaca 59 (2009), no. 4, 499–504. [5] M. Ert¨urk and V. Karakaya, n-tuplet fixed point theorems for contractive type mappings in partially ordered metric spaces, J. Inequal. Appl. 2013 (2013), 368. [6] K. Fan, Extension of two fixed point theorems of F.E. Browder, Math Z. 112 (1969), no. 3, 234–240. [7] T. Gnana Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), no. 7, 1379–1393. [8] J. Guan, Y. Tang, Y. Xu and Y. Su, System of N fixed point operator equations with N-pseudo-contractive mapping in reflexive Banach spaces, J. Nonlinear Sci. Appl. 10 (2017), no. 5, 2457–2470,. [9] W.A. Kirk, S. Reich and P. Veeramani, Proximinal retracts and best proximity pair theorems, Numer. Funct. Anal. Optim. 24 (2003), no. 7-8, 851–862. [10] L.K. Dey and S. Mondal, Best proximity point of F-contraction in complete metric space, Bull. Allahabad Math. Soc. 30 (2015), no. 2, 173–189. [11] S. Mondal and L.K. Dey, Some common best proximity point theorems in a complete metric space, Afr. Mat. 28 (2017), no. 1-2. [12] M. Paknazar, M. Gordji, M.D.L. Sen and S.M. Vaezpour, N-fixed point theorems for nonlinear contractions in partially ordered metric spaces, Fixed Point Theory Appl. 2013 (2013), 111. [13] S. Radenovi´c, Coupled fixed point theorems for monotone mappings in partially ordered metric spaces, Kragujevac J. Math. 38 (2014), no. 2, 249–257. [14] S. Radenovi´c, A note on tripled coincidence and tripled common fixed point theorems in partially ordered metric spaces, Appl. Math. Comput. 236 (2014), 367–372. [15] S. Radenovi´c, Remarks on some recent coupled coincidence point results in symmetric G-metric spaces, J. Oper.2013 (2013), Article ID 290525. [16] T. Senapati, L.K. Dey and D. Doli´canin-Deki´c, Extensions of Ciri´c and Wardowski type fixed point theorems in ´ D-generalized metric spaces, Fixed Point Theory Appl. 2016 (2016), 33. [17] W. Sintunavarat, Y.J. Cho and P. Kumam, Coupled coincidence point theorems for contractions without commutative condition in intuitionistic fuzzy normed spaces, Fixed Point Theory Appl. 2011 (2011), 81. [18] W. Sintunavarat and P. Kuman, Coupled best proximity point theorem in metric spaces, Fixed Point Theory Appl. 2012 (2012), 93. [19] J. Zhang, Y. Su, Q. Cheng, A note on a best proximity point theorem for Geraghty-contractions, Fixed Point Theory Appl. 2013 (2013), 99. [20] Y. Tang, J. Guan, Y. Xu and Y. Su, A kind of system of multivariate variational inequalities and the existence theorem of solutions, J. Inequal. Appl. 2017 (2017), 208. [21] J. Zhang, R.P. Agarwal and N. Jiang, N fixed point theorems and N best proximity point theorems for generalized contraction in partially ordered metric spaces, J. Fixed Point Theory Appl. 20 (2018), no. 1, Article number: 18. | ||
|
آمار تعداد مشاهده مقاله: 16,263 تعداد دریافت فایل اصل مقاله: 10,262 |
||