Common random fixed point theorems for contractions of rational type in ordered metric spaces
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2016-10-14 https://doi.org/10.14419/ijams.v4i2.6577 -
Altering Distance Function, Contractions, Random Fixed Point, Partially Ordered Set, Metric Space. -
Abstract
In this paper, we prove some common random fixed point theorems for mappings involving rational expression in the framework of metric spaces endowed with a partial order using a class of pairs of functions satisfying certain assumptions.
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References
[1] Agarwal, RP, Karapinar, E, & Roldan-Lopez-de-Hierro, AF (2014), Fixed point theorems in quasi-metric spaces and applications, J. Nonlinear Covex Anal.
[2] Altun, I, Simsek, H (2010), some fixed point theorems on ordered metric spaces and application, Fixed Point Theory and Applications, vol.2010, 1-17. Article ID 621469.
[3] Bergiz, M, Karapinar, E, Roldan, A (2014), Discussion on generalized-(αψ, βφ)-contractive mappings via generalized altering distance function and related fixed point theorems, Abstr. Appl. Anal., 2014, Article ID 259768.
[4] Cabrera, I, Harjani, J, Sadarangani, K (2013), A fixed point theorem for contractions of rational type in partially ordered metric spaces. Ann. Univ. Ferrara, 59, 251–258. http://dx.doi.org/10.1007/ s11565-013-0176-x.
[5] Chang, SS, Huang, NJ (1991), on the principle of randomization of fixed points for set valued mappings with applications, North-eastern Math. J., vol.7, 486-491.
[6] Dhage, BC (1999): Condensing mappings and applications to existence theorems for common solution of differential equations, Bull. Korean Math. Soc., vol.36, no.3, 565-578.
[7] Hadzic, O(1979), A random fixed point theorem for multi valued mappings of Ciric’s type. Mat. Vesnik 3 (16) (31), no. 4, 397–401.
[8] Hans, O (1957), Reduzierende Zufallige transformationen, Czech. Math. J. Vol.7, 154-158.
[9] Hans, O (1961), Random operator equations, Proc. 4th Berkeley Symp. Mathematics Statistics and Probability, Vol. II, Part I, pp. 185-202. University of California Press, Berkeley.
[10] Himmelberg, CJ (1975), Measurable relations. Fund. Math. Vol.87, 53-72.
[11] Huang, NJ (1999), a principle of randomization of coincidence points with applications, Applied Math. Lett. 12(1999), 107-113.http://dx.doi.org/10.1016/S0893-9659(98)00157-8.
[12] Itoh, S (1979): Random fixed-point theorems with an application to random differential equations in Banach spaces. J. Math. Anal. Appl. 67(2), 261-273.http://dx.doi.org/10.1016/0022-247X(79)900 23-4.
[13] Joshi, MC, Bose, RK(1984): Some Topics in Nonlinear Functional Analysis. Wiley, New York.
[14] Karapinar, E, Shatanawi, W, Tas, K (2013), Fixed point theorems on partial metric spaces involving rational expressions, Miskolc Math. Notes, 14, 135.142.
[15] Khan, MS, Swaleh, M, Sessa, S (1984), Fixed point theorems by altering distances between the points, Bull. Austr. Math. Soc., 30, 1-9.http://dx.doi.org/10.1017/S0004972700001659.
[16] Liu, TC (1988), Random approximations and random fixed points for non-self-maps, Proc. Amer. Math. Soc., vol.103, 1129-1135.http://dx.doi.org/10.1090/S0002-9939-1988-0954994-0.
[17] Moradi, S, Farajzadeh, A (2012), On the fixed point of (ψ,φ)-weak and generalized (ψ,φ)-weak contraction mappings, Appl. Math. Lett. 25,1257.1262.
[18] Papageorgiou, NS(1984), Random fixed point theorems for multifunctions, Math. Japonica, vol. 29, 93-106.
[19] Papageorgiou, NS (1986), Random fixed point theorems for measurable multifunctions in Banach spaces, Proc. Amer. Math. Soc., vol.97, 507-514. http://dx.doi.org/10.1090/S0002-9939-1986-0840 638-3.
[20] Rocha, J, Rzepka, B, Sadarangani, K (2014), fixed point theorems for contraction of rational type with PPF dependence in Banach Spaces. Journal of Function Spaces, Article ID 416187, 1-8.http://dx.doi.org/10.1155/2014/416187.
[21] Rockafellar, RT (1969), Measurable dependence of convex sets and functions in parameters, J. Math. Anal. Appl., vol.28, 4-25. http://dx.doi.org/10.1016/0022-247X(69)90104-8.
[22] Saluja, AS, Khan, MS, Jhade, PK, Fisher, B (2015), some fixed point theorems for mappings involving rational type expressions in partial metric spaces. Applied Mathematics E-Notes, 15.
[23] Saluja, AS, Rashwan, RA, Magarde, D, Jhade, PK (2016), Some Result in Ordered Metric Spaces for Rational Type Expressions, Facta Universitatis, Ser. Math. Inform. Vol. 31, No 1, 125-138.
[24] Sehgal, VM, Singh, SP (1985), on random approximations and a random fixed point theorem for set valued mappings, Proc. Amer. Math. Soc., vol.95, 91-94.http://dx.doi.org/10.1090/S0002-9939-1985-0796453-1.
[25] Shahzad, N, Latif, A (2000), A random coincidence point theorem, J. Math. Anal. Appl., vol.245, 633-638.http://dx.doi.org/10.1006/ jmaa.2000.6772.
[26] Spacek, a (1955), Zufallige Gleichungen, Czech Math. J., vol.5, 462-466.
[27] Tan, KK, Yuan, XZ, Huang, NJ (1994), Random fixed point theorems and approximations in cones, J. Math. Anal. Appl., vol.185, 378-390.http://dx.doi.org/10.1006/jmaa.1994.1256.
[28] Wagner DH (1977), Survey of measurable selection theorems, SIAM, J, Control Optim., vol.15, 859-903.http://dx.doi.org/10.1137 /0315056.
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How to Cite
Singh, S. R., daheriya, R. D., & Ughade, M. (2016). Common random fixed point theorems for contractions of rational type in ordered metric spaces. International Journal of Advanced Mathematical Sciences, 4(2), 37-43. https://doi.org/10.14419/ijams.v4i2.6577