The Existance of the Optimum Solution for the System of Differential Equation in Hilbert Space
Subject Areas : Statistics
1 - Department of Mathematical Sciences, University of Kashan, Ravand Road, Kashan, Iran
Keywords: دستگاه معادلات دیفرانسیل, دستگاه تکامل انقباضی, نقاط بهترین تقریب, فضای هیلبرت,
Abstract :
In this paper, we study the existence of the following optimum solution for the system of differential equation ...
[1] A. Abkar, M. Gabeleh, Best proximity points for asymptotic cyclic contraction mappings, Nonlinear Anal, 74 (2011), no. 18, 7261-7268.
[2] A. Abkar, M. Gabeleh, Best proximity points for cyclic mappings in ordered metric spaces, J. Optim. Theory Appl, 151 (2011), 418-424.
[3] A. Al-Thagafi, N. Shahzad, Convergence and existence results for best proximity points, Nonlinear Anal, 70 (2009), 3665-3671.
[4] C. Di Bari, T. Suzuki, C. Vetro, Best proximity points for cyclic Meir--Keeler contractions, Nonlinear Anal, 69 (2008), 3790-3794.
[5] M. Derafshpour, S. Rezapour, and N. Shahzad, Best proximity points of cyclic-contractions in ordered metric spaces, Topological Methods in Nonlinear Analysis, 37 (2011), 193-202.
[6] A. A. Eldred, P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl, 323 (2006), 1001-1006.
[7] R. Espinola, A. Fernandez-Leon, On best proximity points in metric and Banach spaces, Canad. J. Math, 63 (2011), no. 3, 533-550.
[8] A. Fernandez-Len, Existence and uniqueness of best proximity points in geodesic metric spaces, Nonlinear Anal, 73 (2010), no. 4, 915-921.
[9] M. Kamenskii, V. Obukhovskii, P. Zecca, Condensing multivalued maps and semilinear differential inclusions in Banach spaces, De Gruyter Series in Nonlinear Analysis and Applications. 7, Walter de Gruyter Co., Berlin, 2001.
[10] S. Karpagam, S. Agrawal, Best proximity point theorems for p-cyclic Meir-Keeler contractions, Fixed Point Theory and Applications, 70 (2009), 3332-3341.
[11] W.A. Kirk, P.S. Srinivasan, P. Veeramani, Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory, 4 (2003), 79-89.
[12] B. Piatek, On cyclic Meir-Keeler contractions in metric spaces, Nonlinear Anal, 74 (2011), no. 1, 35-40.
[13] T. Suzuki, M. Kikkawa, C. Vetro, The existence of best proximity points in metric spaces with the property UC, Nonlinear Anal, 71 (2009), 2918-2926.
[14] P. Veeramani, S. Rajesh, Best Proximity Points. in Q. H. Ansari, Qamrul Hasan Ansari Nonlinear Analysis, Approximation Theory, Optimization and Applications (1-32). Springer New Delhi Heidelberg New York Dordrecht London. 2014.
[15] C. Vetro, Best proximity points: convergence and existence theorems for p-cyclic mappings, Nonlinear Anal, 73 (2010), no. 7, 2283-2292.