Research Journal of Science and Technology

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Coupled Fixed Point of Set Valued Mapping in Partially Ordered G-Metric Space


Affiliations
1 Department of Mathematics, National Institute of Technology, Hamirpur - 177005, India
     

   Subscribe/Renew Journal


In this manuscript, we obtain sufficient condition for the existence of a coupled fixed point of a mixed monotone set-valued bivariate self map F, i.e. F : X × X → X in partially ordered complete G-metric space.

Keywords

Coupled Fixed Point, G-metric Space, Set-valued Maps, Partially Ordered Set.
Subscription Login to verify subscription
User
Notifications
Font Size


  • I. Beg, Random fixed points of increasing compact maps, Archi. Mathematicum 37(2001), 329-332.

  • I. Beg and A. Azam, Fixed points of asymptotically regular multivalued mappings, J. Austral. Math. Soc. (Series-A) 53(3) (1992), 313-326.

  • I. Beg and A.R. Butt, Fixed point for set valued mappings satisfying an implicit relation in partially ordered metric spaces, Nonlinear Anal. 71(2009), 3699-3704.

  • I. Beg and A.R. Butt, Fixed points for weakly compatible mappings satisfying an implicit relation in partially ordered metric spaces, Carpathian J. Math. 25(2009), 1-12.

  • I. Beg and A.R. Butt, Common Fixed point for generalized set valued contractions satisfying an implicit relation in partially ordered metric spaces, Mathematical Communications, 15(2010), 65-76.

  • I. Beg, A. Latif, R. Ali and A. Azam, Coupled Fixed points of mixed monotone operators on probabilistic Banach spaces, Archivum Mathematicum 37(2001), 1-8.

  • T.G. Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379- 1393.

  • P.Z. Daffer, Fixed points of generalized contractive multivalued mappings, J. Math. Anal. Appl., 192 (1995), 655-666.

  • P.Z. Daffer, H. Kaneko and W. Li, On a conjecture of S. Reich, Proc. Amer. Math. Soc., 124 (1996), 3159-3162.

  • Y. Feng and S. Liu, Fixed point theorems for multivalued contractive mappings and multivaled Caristi type mappings, J. Math. Anal. Appl., 317 (2006), 103-112.

  • D. Guo and V. Lakshmikantham, Coupled Fixed points of nonlinear operators with applications, Nonlinear. Anal., 11(1987), 623-632.

  • J. Harjani, K. Sadarangani, Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Anal. 71(2009), 3403-3410.

  • J. Harjani, K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal. (2009), doi:10.1016/j.na.2009.08.003(in press).

  • W.A. Kirk and K.Goebel, Topics in Metric Fixed Point Theory, Cambridge University Press, Cambridge (1990).

  • D. Klim and D.Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl., 334 (2007), 132-139.

  • A. Kaewcharoen and A. Kaewkhao, Common Fixed Points for Single- Valued and Multi-Valued Mappings in G-Metric Spaces, Int. Journal of Math. Analysis, 536 (2011), 1775-1790.

  • Z. Mustafa and B. Sims, Some remarks concerning D-metric spaces, Proceedings of the International Conferences on Fixed Point Theory and Applications, Valencia (Spain) (2003), 185-198. 18. S.B. Nadler, Multivalued contraction mappings, Pacific J. Math., 30(1969), 475-488.

  • J.J. Nieto, R.L. Pouso and R. Rodriguez-Lopez, Fixed point theorems in ordered abstract spaces, Proc. Amer. Math. Soc., 135(2007), 2505-2517.

  • J.J. Nieto and R. Rodriguez-Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22(2005), 223-239.

  • J.J. Nieto and R. Rodriguez-Lopez, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta. Math. Sinica, (English Ser.) 23(2007), 2205-2212.

  • D. O'Regan and A. Petrusel, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl., 341 (2008), 1241-1252.

  • A. Petrusel and I.A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math.Soc., 134 (2005), 411-418.

  • C.Y. Qing, On a fixed point problem of Reich, Proc. Amer. Math. Soc., 124 (1996), 3085-3088.

  • A.C.M. Ran and M.C.B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1435-1443.

  • S. Reich, Fixed points of contractive functions, Boll. Unione. Mat. Ital., 4 (1972), 26-42.

  • Y. Wu, New fixed point theorems and applications of mixed monotone operator, J. Math. Anal. Appl., 341 (2008), 883-893.

  • E. Zeidler, Nonlinear Functional Analysis and its Applications I, Fixed point Theorems, Springer Verlag, New York (1985).

  • Z. Zhitao, New fixed point theorems of mixed monotone operators and applications, J.Math. Anal. Appl., 204 (1996), 307-319.


Abstract Views: 800

PDF Views: 0




  • Coupled Fixed Point of Set Valued Mapping in Partially Ordered G-Metric Space

Abstract Views: 800  |  PDF Views: 0

Authors

Ramesh Kumar Vats
Department of Mathematics, National Institute of Technology, Hamirpur - 177005, India
Amit Kumar
Department of Mathematics, National Institute of Technology, Hamirpur - 177005, India
J. Ravinder
Department of Mathematics, National Institute of Technology, Hamirpur - 177005, India

Abstract


In this manuscript, we obtain sufficient condition for the existence of a coupled fixed point of a mixed monotone set-valued bivariate self map F, i.e. F : X × X → X in partially ordered complete G-metric space.

Keywords


Coupled Fixed Point, G-metric Space, Set-valued Maps, Partially Ordered Set.

References