تعداد نشریات | 27 |
تعداد شمارهها | 558 |
تعداد مقالات | 5,776 |
تعداد مشاهده مقاله | 8,031,842 |
تعداد دریافت فایل اصل مقاله | 5,398,757 |
Coupled common fixed point theorems for $varphi$-contractions in probabilistic metric\ spaces and applications | ||
Iranian Journal of Fuzzy Systems | ||
مقاله 6، دوره 12، شماره 6، اسفند 2015، صفحه 95-108 اصل مقاله (381.84 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2015.2182 | ||
نویسندگان | ||
S. H. Wang1؛ A. A. N. Abdou2؛ Y. J. Cho* 3 | ||
1Department of Mathematics and Physics, North China Electric Power University, Baoding, China | ||
2Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia | ||
3Department of Education Mathematics and RINS, Gyeongsang National University, Jinju, Korean | ||
چکیده | ||
In this paper, we give some new coupled common fixed point theorems for probabilistic $varphi$-contractions in Menger probabilistic metric spaces. As applications of the main results, we obtain some coupled common fixed point theorems in usual metric spaces and fuzzy metric spaces. The main results of this paper improve the corresponding results given by some authors. Finally, we give one example to illustrate the main results of this paper. | ||
کلیدواژهها | ||
Menger probabilistic metric space؛ probabilistic $varphi$-contraction؛ coupled fixed points | ||
مراجع | ||
[1] T. G. Bhashkar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379{1393. [2] S. S. Chang, Y. J. Cho and S. M. Kang, Nonlinear Operator Theory in Probabilistic Metric Spaces, Nova Science Publishers, Inc., New York, 2001. [3] B. S. Choudhury, K. Das and P. N. Dutta, A xed point result in Menger spaces using a real function, Acta Math. Hungar., 122 (2009), 203{216. [4] B. S. Choudhury and A. Kundu, A coupled coincidence point result in partially ordered metric spaces for compatible mappings, Nonlinear Anal., 73 (2010), 2524{2531. [5] L. B. Ciric, Solving the Banach xed point principle for nonlinear contractions in probabilistic metric spaces, Nonlinear Anal., 72 (2010), 2009{2018. [6] L. B. Ciric, R. P. Agarwal and B. Samet, Mixed monotone-generalized contractions in par- tially ordered probabilistic metric spaces, Fixed Point Theory Appl., (2011) 2011:56. [7] L. B. Ciric, D. Mihet and R. Saadati, Monotone generzliaed contractions in partially ordered probabilistic metric spaces, Topology Appl., 156 (2009), 2838{2844. [8] J. X. Fang, Fixed point theorems of local contraction mappings on Menger spaces, Appl. Math. Mech., 12 (1991), 363{372. [9] J. X. Fang, Common xed point theorems of compatible and weakly compatible maps in Menger spaces, Nonlinear Anal., 71 (2009), 1833{1843. [10] J. X. Fang, On '-contractions in probabilistic and fuzzy metric spaces, Fuzzy Sets Syst., 267 (2014), 86{99. [11] O. Hadzic and E. Pap, Fixed Point Theory in PM-Spaces, Kluwer Academic Publ., 2001. [12] X. Q. Hu, Common coupled xed point theorems for contractive mappings in fuzzy metric spaces, Fixed Point Theory Appl., Article ID 363716 (2011), 2011. [13] J. Jachymski, On probabilistic '-contractions on Menger spaces, Nonlinear Anal., 73 (2010), 2199{2203. [14] K. Karapinar, Coupled xed point theorems for nonlinear contractions in cone metric spaces, Comput. Math. Appl., 59 (2010), 3656{3668. [15] I. Kramosi and J. Michalek, Fuzzy metrics and statistical metric spaces, Kybernetika, 11 (1975), 336{344. [16] V. Lakahmikantham and L. B. Ciric, Coupled xed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70 (2009), 4341{4349. [17] N. V. Luong and N. X. Thuan, Coupled xed points in partially ordered metric spaces and application, Nonlinear Anal., 74 (2011), 983{992. [18] K. Menger, Statistical metric, Proc Natl. Acad. USA., 28 (1942), 535{537. [19] D. O'Regan and R. Saadati, Nonlinear contraction theorems in probabilistic spaces, Appl. Math. Comput., 195 (2008), 86{93. [20] R. Saadati, Generalized distance and xed point theorems in partially ordered probabilistic metric spaces, Mate. Vesnik, 65 (2013), 82{93. [21] B. Samet, Coupled xed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal., 71 (2010), 4508{4517. [22] B. Schweizer and A. Sklar, Probabilisitc Metric Spaces, Elsevier/North-Holland, New York, 1983. [23] S. Sedghi, I. Altun and N. Shobec, Coupled xed point theorems for contractions in fuzzy metric spaces, Nonlinear Anal., 72 (2010), 1298{1304. [24] V. M. Sehgal and A. T. Bharucha-Reid, Fixed points of contraction mappings on probabilistic metric space, Math Syst. Theory, 6 (1972), 87{102. [25] J. Z. Xiao, X. H. Zhu and Y. F. Cao, Common coupled xed point results for probabilistic '-contractions in Menger spaces, Nonlinear Anal., 74 (2011), 4589{4600. | ||
آمار تعداد مشاهده مقاله: 1,693 تعداد دریافت فایل اصل مقاله: 1,153 |