Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 7 (2012), 137 -- 145

EXISTENCE AND DATA DEPENDENCE FOR MULTIVALUED WEAKLY REICH-CONTRACTIVE OPERATORS

Liliana Guran Manciu

Abstract. In this paper we define the concept of weakly Reich-contractive operator and give a fixed point result for this type of operators. Then we study the data dependence for this new result.

2010 Mathematics Subject Classification: 47H10; 54H25
Keywords: w-distance, τ-distance, weakly Reich-contraction, fixed point, multivalued operator

Full text

References

  1. A. Granas, J. Dugundji, Fixed Point Theory, Berlin, Springer-Verlag, 2003.

  2. Y. Feng, S. Liu, Fixed point theorems for multivalued contractive mappings and multivalued Caristi type mappings, J. Math. Anal. Appl. 317(2006), 103-112. Zbl 1094.47049.

  3. L. Guran, Existence and data dependence for multivalued weakly contractive operators, Studia Univ. Babeş-Bolyai, Mathematica, 54(2009), no. 3, 67-76.

  4. O. Kada, T. Suzuki, W. Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japonica 44(1996) 381-391. MR1416281(97j:49011). Zbl 0897.54029.

  5. A. Latif, A.W. Albar , Fixed point results for multivalued maps, Int. J. Contemp. Math. Sci. 2, 21-24(2007), 1129-1136. MR2373908. Zbl 1165.54018.

  6. A. Latif, A. A. N. Abdou, Fixed point results for generalized contractive multimaps in metric spaces, Fixed Point Theory and Applications Volume 2009(2009), Article ID 432130, 16 pages doi:10.1155/2009/432130. MR2544343. Zbl 1179.54065.

  7. A. Latif, Saleh Abdullah Al-Mezel, Fixed point results related to Reich'S problem, Fixed Point Theory and Applications, Vol.4(2009), Issue 2, 147-159.

  8. T. Lazăr, A. Petruşel, N. Shahzad, Fixed points for non-self operators and domanin invariance theorems, Nonlinear Analysis: Theory, Methods and Applications, 70(2009), 117-125.

  9. S. Reich, Fixed points of contractive functions, Boll. Unione Mat. Ital., 5(1972), 26-42.

  10. S. Reich, A. J. Zaslavski, Convergence of iterates of nonexpansive set-valued mappings, Set Valued Mappings with Applications in Nonlinear Analysis, 4(2002) of Mathematical Analysis and Applications, 411--420, Taylor and Francis, London, UK.

  11. S. Reich, A. J. Zaslavski, Generic existence of fixed points for set-valued mappings, Set-Valued Analysis, 10(2002), no. 4, 287--296.

  12. S. Reich, A. J. Zaslavski, Two results on fixed points of set-valued nonexpansive mappings, Revue Roumaine de Mathématiques Pures et Appliquées, 51(2006), no. 1, 89--94.

  13. S. Reich, A. J. Zaslavski, Existence and Approximation of Fixed Points for Set-Valued Mappings, Fixed Point Theory and Applications, Volume 2010(2010), Article ID 351531, 10 pages doi:10.1155/2010/351531. Zbl 1189.54037

  14. I. A. Rus, Generalized Contractions and Applications, Presa Clujeană Universitară, Cluj-Napoca, 2001.

  15. T. Suzuki, Generalized Distance and Existence Theorems in Complete Metric Spaces, J.Math.Anal.Appl., 253(2001), 440-458. MR1808147(2002f:49038). Zbl 0983.54034.

  16. T. Suzuki, Several Fixed Point Theorems Concerning τ-distance, Fixed Point Theory and Application, 3(2004), 195-209. MR2096951. Zbl 1076.54532.

  17. T. Suzuki, W. Takahashi, Fixed points theorems and characterizations of metric completeness, Topological Methods in Nonlinear Analysis, Journal of Juliusz Schauder Center, 8(1996), 371-382. MR1483635(99c:54064). Zbl 0902.47050.


Liliana Guran Manciu
Department of Finance and Business Administration,
Faculty of Economic Sciences, Titu Maiorescu University,
Calea Văcăreşti, nr. 189, 040056, sector 4, Bucharest, Romania.
e-mail: liliana.guran@utm.ro, gliliana.math@gmail.com.

http://www.utgjiu.ro/math/sma