آمار
| تعداد نشریات | 26 |
| تعداد شماره‌ها | 447 |
| تعداد مقالات | 4,557 |
| تعداد مشاهده مقاله | 5,380,005 |
| تعداد دریافت فایل اصل مقاله | 3,580,078 |
Generalizations of Banach's contraction principle and Kannan and Chatterjea's theorems for cyclic and non-cyclic mappings | ||
| Journal of Mahani Mathematical Research | ||
| دوره 12، شماره 2 - شماره پیاپی 25، مرداد 2023، صفحه 349-362 اصل مقاله (499.04 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2023.19871.1298 | ||
| نویسنده | ||
| Akram Safari-Hafshejani* | ||
| Department of Pure Mathematics, Payame Noor University, P. O. Box: 19395-3697, Tehran, Iran | ||
| چکیده | ||
| Two interesting extensions of Banach contraction principle to mappings that don't to be continuous, are Kannan and Chatterjea's theorems. Before this, in the cyclical form, extensions of these two theorems and Banach contraction principle were produced. But so far, these theorems have not been studied in the noncyclical form. In this paper, we answer the question whether there are versions of these theorems for noncyclic mappings, also we give generalizations of existing results. For this purpose, in the setting of metric spaces we introduce the notions of cyclic and non-cyclic contraction of Fisher type. We establish the existence of fixed points for these mappings and iterative algorithms are furnished to determine such fixed points. As a result of our results we give new Theorems for cyclic orbital contractions. | ||
| کلیدواژه‌ها | ||
| Fixed point؛ Cyclic and non-cyclic contractions of Fisher-type؛ Kannan and Chatterjea mappings؛ cyclic orbital contraction | ||
| مراجع | ||
|
[1] A. Abkar, M. Gabeleh, Proximal quasi-normal structure and a best proximity point theorem, J. Nonlinear Convex Anal. vol. 14, no. 4 (2013) 653{659.
[2] S. K. Chatterjea, Fixed point theorems, C. R. Acad. Bulgare Sci. vol. 25 (1972) 727{730.
[3] CM. Chen, Fixed point theorems of generalized cyclic orbital Meir-Keeler contractions, Fixed Point Theory Appl. vol. 91 (2013) 10 pages.
[4] Lj. B. Ciric, A generalization of Banach's contraction principle, Proc. Amer .Math. Soc. vol. 45, no. 2 (1974) 267{273.
[5] R. Espnola, A. Fernandez-Leon, On best proximity points in metric and Banach space, Canad. J. math. vol. 63, no. 3 (2011) 533{550.
[6] A. Fernandez-Leon, M. Gabeleh, Best proximity pair theorems for noncyclic mappings in Banach and metric spaces, Fixed Point Theory vol. 17, no. 1 (2016) 63{84.
[7] B. Fisher, Quasicontractions on metric spaces, Proc. Amer. Math. Soc. vol. 75, no.2 (1979) 321{325.
[8] M. Gabeleh, Best proximity points and xed point results for certain maps in Banach spaces, Numer. Funct. Anal. Optim. vol. 36 (2016) 167{188.
[9] M. Gabeleh, N. Shahzad, Best proximity pair and xed point results for noncyclic mappings in convex metric spaces, Filomat vol. 30, no. 12 (2016), 3149{3158.
[10] R. Kannan, Some results on xed points, Bull. Calcutta Math. Soc. vol. 10 (1968) 71{76.
[11] E. Karapinar, H. K. Nashine, Fixed point theorem for cyclic Chatterjea type contractions, J. Appl. Math. vol. 2012 (2012) 15 pages.
[12] E. Karapinar, S. Romaguera, K. Tas, Fixed points for cyclic orbital generalized contractions on complete metric spaces Cent. Eur. J. Math. vol. 11 (2013) 552{560.
[13] S. Karpagam, S. Agrawal, Best proximity point theorems for cyclic orbital Meir-Keeler contraction maps, Nonlinear Anal. vol. 74 (2011) 1040{1046.
[14] S. Karpagam, B. Zlatanov, Best proximity point of p-cyclic orbital Meir-Keeler contraction maps, Nonlinear Anal. Model. Control vol. 21, no. 6 (2016) 790{806.
[15] F. Kiany, A. Amini-Harandi, Fixed point theory for generalized Ciric quasi-contraction maps in metric spaces, Fixed Point Theory Appl. vol. 26 (2013) 6 pages.
[16] W. A. Kirk, P. S. Srinivasan, P. Veeramani, Fixed points for mappings satisfying cylical contractive contractions, Fixed Point Theory vol. 4, no. 1 (2003) 79{89.
[17] P. Kumam, N. V. Dung, K. Sitthithakerngkiet, A generalization of Ciric xed point theorems, Filomat vol. 29, no. 7 (2015) 1549{1556.
[18] M. A. Petric, Best proximity point theorems for weak cyclic Kannan contractions, Filomat vol. 25 (2011) 145{154. [19] M. Petric, B. G. Zlatanov, Fixed point theorems of Kannan type for cyclical contractive conditions, University Press Paisii Hilendarski, (Plovdiv, Bulgaria 2010). [20] T. Suzuki, M. Kikawa, C. Vetro, The existence of best proximity points in metric spaces with the property UC, Nonlinear Anal. vol. 71 (2009) 2918{2926. | ||
|
آمار تعداد مشاهده مقاله: 198 تعداد دریافت فایل اصل مقاله: 299 |
||