Coupled points for total weakly contraction mappings via Ï-distance

  • Authors

    • Salwa Abed Baghdad university, College of Education for pure sciences, Ibn Al-Haitham, department of mathematics
    • Hiba Adel Jabbar
    2016-07-09
    https://doi.org/10.14419/ijbas.v5i3.6222
  • Weak Contractions, Coupled Fixed Points, Coupled Coincidence Points, General Metric Spaces.

  • Abstract

    In this paper, the total weakly contraction mappings and T-total weakly contraction mappings are defined with respect to Ï-distance. The concepts of mixed monotone and general mixed monotone are used to prove some theorems about coupled fixed points, common fixed point and coincidence points for these mappings in partially general b-metric spaces which equipped with Ï-distance.


    Author Biography

    • Salwa Abed, Baghdad university, College of Education for pure sciences, Ibn Al-Haitham, department of mathematics

      Dr. Salwa S.Abed, assist.proff.in Dep. of math.

       

  • References

    1. [1] Abbasa M., Khanb A.R., Nazira T., common fixed point of multivalued mappings in ordered generalized metric spaces, Filomat 26:5, pp. 1045-1053, (2012).

      [2] Abed S.S., Gassem A.A., fixed point theorem for uncommuting mappings, Ibn Al-Haitham J. For Pure Sciences and Applied Sciences, Vol.26, no.1, (2013).

      [3] Abed S.S., Gassem A.A., two fixed point theorems in orbitally complete generalized metric space, Al- Qadisiya J. For Sciences Vol 17, no.4, pp142-155, (2012).

      [4] Abed S.S., Jabbar H.A., coupled points for total weakly contraction mappings via -m space, inter. J. of advan. Scie. and tech. resear., Issur 6, vol.3, pages 64-79, (2016).

      [5] Aghajani A., Abbas M., Roshan J.R., common fixed point of generalized weak contraction mappings in partially ordered b-metric spaces, Math. Slovaca, in press.

      [6] Aydi H., Bota M.F., Karapinar E., Mitrovic S., a fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory Appl. 2012:88, (2012).http://dx.doi.org/10.1186/1687-1812-2012-88.

      [7] Bhaskar T.G., Lakshmikantham V., fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal.TMA 65, 1379-1393, (2006).

      [8] Boriceanu M., fixed point theory for multivalued generalized contraction on a set with two b-metrics, Studia Univ. Babes Bolyai, Mathematica, Vol. Liv, No.3, (2009).

      [9] Boriceanu M., strict fixed point theorems for multivalued operators in b-metric spaces, Int. J. Modern Math. 4(3), 285-301, (2009).

      [10] Branciari A., a fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, publ. Math. Debrcen, 57:1-2, 31-37, (2000).

      [11] Ciric L., Hussain N., Akbar F., Ume J., common fixed point for Banach operator pairs from the set of best approximations, Bull. Belg. Math. Soc. Simon Stevin 16, 319-336, (2009).

      [12] Ciric L., Hussain N., Cakic N., common fixed points for Ciric type f-weak contraction with applications, Publ. Math. (Debr.) 76(1-2), 31-49, (2012).

      [13] Cvetkovic A.S., Stanic M.P., Dimitrijevic S., Simic S., common fixed point theorems for four mappings on cone metric type space, Fixed Point Theorem Appl., Art. ID 589725, (2011).

      [14] Czerwik S., contraction mappings in b-metric spaces, Acta Math. Univ. Ostrav. 1, 5-11, (1993).

      [15] Gassem A.A., some result about fixed points in some metric spaces, M. Sc. Thesis, College Of Education Ibn-Haitham For Pure Sciences. Baghdad University, (2012).

      [16] Rhoades B.E., Abbas M., necessary and sufficient condition for common fixed point theorems, J. Adv. Math. Stud. 2(2), 97-102, (2009).

      [17] Hussain N., Djoric D., Kadelburg Z., Radenovic, Suzuki S., type fixed point results in metric type spaces. Fixed point Theory Appl., Article ID 126, (2012).

      [18] Kada O., Suzuki T., Takahashi W., non-convex minimization theorems and fixed point theorems in complete metric spaces, Mathematica Japonica, vol. 44, no. 2, pp. 381-391, (1996).

      [19] Laksmikantham V., Ciric L., coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Nonlinear Anal. 70, 4341-4349, (2009).http://dx.doi.org/10.1016/j.na.2008.09.020.

      [20] Mustafa Z., Roshan J.R., Parvaneh V., coupled coincidence point results for (ψ ,φ)-weakly contractive mappings in partially ordered -metric spaces, Fixed Point Theory Appl., 206. (2013).http://dx.doi.org/10.1186/1687-1812-2013-206.

      [21] Mustafa Z., Sims B., a new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7, 289-297, (2006).

      [22] Nashine H.K., Shatanawi W., coupled common fixed point theorems for pair of commuting mappings in partially ordered complete metric spaces, Comput. Math. Appl. 62(4), 1984-1993, (2011).http://dx.doi.org/10.1016/j.camwa.2011.06.042.

      [23] Parvaneh V., Roshan J.R., Radenović S., existence of tripled coincidence points in ordered b-metric spaces and an application to a system of integral equations, Fixed Point Theory Appl. 2103:130, (2013).http://dx.doi.org/10.1186/1687-1812-2013-130.

      [24] Roshan J.R., Parvaneh V., Sedghi S., Shobe N., Shatanawi W., common fixed points of almost generalized (ψ ,φ)-contractive mappings in ordered b-metric spaces, Fixed Point Theory Appl. 2103:159, (2013).http://dx.doi.org/10.1186/1687-1812-2013-159.

      [25] Saadati R., Vaezpour S.M., Vetro P., Rhoades B.E., fixed point theorems in generalized partially ordered G-metric spaces, Math. Comput. Modelling. 52,797-801, (2010).http://dx.doi.org/10.1016/j.mcm.2010.05.009.

      [26] Sabetghadam F., Masiha H.P., Sanatpour A.H., some coupled fixed point theorems in cone metric spaces, Fixed point Theory and Applications, vil. 2009, Article ID 125426, 8 pages, (2009).

      [27] Tahat N., Aydi H., Karapinar E., Shatanawi W., common fixed points for single-valued and multi-valued maps satisfying a generalized contraction in G-metric spaces, Fixed Point Theory Appl. 2012, Article ID 48, (2012).http://dx.doi.org/10.1186/1687-1812-2012-48.

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  • How to Cite

    Abed, S., & Jabbar, H. A. (2016). Coupled points for total weakly contraction mappings via ρ-distance. International Journal of Basic and Applied Sciences, 5(3), 164-171. https://doi.org/10.14419/ijbas.v5i3.6222

    Received date: 2016-05-09

    Accepted date: 2016-06-02

    Published date: 2016-07-09