Approximation of Random Fixed Point Theorems
DOI:
https://doi.org/10.5890/DNC.2018.03.008Abstract
The aim of this paper is to establish and discuss the approximation of Caristi’s random fixed point theorems. Our theorem is used to determine a large numbers of nonlinear stochastic problems.References
[1] Spacek, A. (1955), Zufallige gleichungen, Czechoslovak Math., 5, 462-466.
[2] Hans, O. (1957), Reduzierende zulliallige transformaten, Czechoslovak Math. J., 7, 154-158.
[3] Hans, O. (1961), Random operator equations, Proceedings of the fourth Berkeley Symposium on Math., Statistics and Probability II, Part I, 85-202.
[4] Tsokos, C.P. (1969), On a stochastic integral equation of the Volterra type, Math. Systems Theory, 3, 222-231.
[5] Tsokos, C.P. and Padgett, W.J. (1971), Random Integral Equations with Applications to Stochastic Sytems, Lecture Notes in Mathematics, Springer, Berlin, Germany, 233 .
[6] Tsokos, C.P. and Padgett,W.J. (1974), Random Integral Equations with Applications to Life Sciences and Engineering, Academic Press, New York.
[7] Cho, Y.J., Khan, M.F., and Salahuddin (2006), Notes on random fixed point theorems, J. Korea Soc. Math. Educ. Ser.B: Pure and Applied Mathematics, 13(3), 227-236.
[8] Ahmad, M.K. and Salahuddin (2010), Collectively random fixed point theorems and application, PanAmer Math. J., 20(3), 69-84.
[9] Itoh, S. (1979), Random fixed point theorems with an application to random differential equations in Banach spaces, J. Math. Anal. Appl., 67, 261-273.
[10] Bharucha-Reid, A.T. (1972), Random Integral Equations, Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 9.
[11] Bharucha-Reid, A.T. (1976), Fixed point theorems in probabilistic analysis, Bull. Amer. Math. Soc., 82, 64-65.
[12] de Blasi, F.S., Myjak, J., Reich, S., and Zaslavski, A.J. (2009), Generic existence and approximation of fixed points for non ensive set valued maps, Set Valued Var. Anal., 17, 97-112.
[13] Kirk,W.A. (2001), Contraction mappings and extensions, Handbook of Metric Fixed Point Theory, Dordrecht, 1-34.
[14] Lee, B.S., Farajzadeh, A., and Salahuddin (2015), On PPF dependent fixed point theorems and applications, J. Concrete Applicable Math., 13(1-2), 69-75.
[15] Mordukhovich, B.S. (2006), Variational Analysis and Generalized Differentiation, 1, Basi Theory, Springer, Berlin.
[16] Reich, S. and Zaslavski, A.J. (2014), Genericity in Nonlinear Analysis, Developments in Mathematics, 34, Springer, New York.
[17] Reich, S. and Zaslavski, A.J. (2015), Variants of Caristi's fixed point theorem, PanAmer. Math. J., 25(1), 42-52.
[18] Ahmad, M.K. (2008), and Salahuddin, Random variational like inequalities, Adv. Nonlinear Var. Inequal., 11(2), 15-24.
[19] Caristi, J. (1976), Fixed point theorems for maps satisfying inwardness conditions, Trans. Amer. Math. Soc., 215, 241-251.
[20] Kim, J.K. and Salahuddin (2015), The existence of deterministic random generalized vector equilibrium problems, Nonlinear Funct. Anal. Appl., 20(3), 453-464.
[21] Goudarzi, H.R. (2014), Random fixed point theorems in Frechet spaces with their applications, J. Math. Ext., 8(2), 71-81.
[22] Himmelberg, C.J. (1975), Measurable relations, Fund. Math., 87, 53-72.
[23] Hussain, S., Khan, M.F., and Salahuddin (2004), Strongly nonlinear mixed random variational inequalities, International J. Math. Sci., 3(2), 361-368.
[24] Khan, M.F. and Salahuddin (2006), Completely generalized nonlinear random variational inclusions, Southeast Asian Bull. Math., 30(5), 261-276.
[25] Papagergiou, N.S. (1986), Random fixed point theorems for measurable multifunction in Banach spaces, Proc. Amer. Math. Soc., 97(1), 507-514.
[26] Salahuddin (2016), General random variational inequalities and applications, Transact. Math. Prog. Appl., 4(1), 25-33.
[27] Siddiqi, A.H., Ahmad, M.K., and Salahuddin (2008), Applications of randomly pseudomonotone operators with randomly upper semicontinuity in generalized random quasi-variational inequalities, J. Appl. Funct. Anal., 3(1), 33-50.
[28] Tan, K.K. and Yuan, X.Z. (1994), Random fixed point theorems and approximation in cones, J. Math. Anal Appl., 185, 378-390.
[29] Verma, R.U., Khan, M.F., and Salahuddin, (2006), Generalized random variational like inequalities with randomly pseudomonotone multivalued mappings, PanAmer. Math. J., 16(3), 33-46.
[30] Verma, R.U. and Salahuddin, (2013), A common fixed point theorem for fuzzy mappings, Transact. Math. Prog. Appl., 1(1), 59-68.
[31] Verma, R.U. and Salahuddin (2016), Existence of random variational inequalities, PanAmer. Math. J., 26(2), 95-103.
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