Coincidence point theorems for multivalued f-weak contraction mappings and applications

• Autores: M. Abbas, N. Hussain, B.E. Rhoades
• Localización: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas ( RACSAM ), ISSN-e 1578-7303, Vol. 105, Nº. 2, 2011, págs. 261-272
• Idioma: inglés
• DOI: 10.1007/s13398-011-0036-4
• Texto completo no disponible (Saber más ...)
• Resumen

  • We prove the existence of coincidence points and common fixed points for multivalued f-weak contraction mappings which assume closed values only. As an application, related common fixed point, invariant approximation, random coincidence point and random invariant approximation results are also obtained. Our results provide extensions as well as substantial improvements of several well known results in the existing literature. © 2011 Springer-Verlag.

• Referencias bibliográficas
  • Al-Thagafi, M.A., Common fixed points and best approximation (1996) J. Approx. Theory, 85, pp. 318-320
  • Al-Thagafi, M.A., Shahzad, N., Noncommuting self maps and invariant approximations (2006) Nonlinear Anal., 64, pp. 2778-2786
  • Al-Thagaf, M.A., Shahzad, N., Coincidence points, generalized I-nonexpansive multimaps and applications Nonlinear Anal, , (in press
  • Beg, I., Khan, A.R., Hussain, N., Approximation of *-nonexpansive random multivalued operators on Banach spaces (2004) J. Austral. Math....
  • Beg, I., Abbas, M., Iterative procedures for solution of random equations in Banach spaces (2006) J. Math. Anal. Appl., 315, pp. 181-201
  • Berinde, V., Approximating fixed points of weak contraction using the Picard iteration (2004) Nonlinear Anal. Forum., 9, pp. 43-53
  • Berinde, M., Berinde, V., On general class of multivalued weakly Picard mappings (2011) J. Math. Anal. Appl, , (in press
  • Fierro, R., Martnez, C., Morales, C.H., Fixed point theorems for random lower semi-continuous mappings (2009) Fixed Point Theory Appl. 2009,...
  • Himmelberg, C.J., Measurable relations (1975) Fund. Math., 87, pp. 53-72
  • Hussain, N., Coincidence points for multivalued maps defined on non-starshaped domain (2006) Demo. Math. Demo. Math., 39, pp. 579-584
  • Hussain, N., Jungck, G., Common fixed point and invariant approximation results for noncommuting generalized (f, g) -nonexpansive maps (2006)...
  • Hussain, N., O'Regan, D., Agarwal, R.P., Common fixed point and invariant approximation results on non-starshaped domains (2005) Georgian...
  • Itoh, S., Random fixed point theorems with an application to random differential equations in Banach spaces (1979) J. Math. Anal. Appl.,...
  • Jungck, G., Commuting mappings and fixed points (1976) Am. Math. Mon., 83, pp. 261-263
  • Jungck, G., Common fixed points for commuting and compatible maps on compacta (1988) Proc. Am. Soc., 103, pp. 977-983
  • Jungck, G., Coincidence and fixed points for compatible and relatively nonexpansive maps (1993) Int. J. Math. Math. Sci., 16, pp. 95-100
  • Jungck, G., Rhoades, B.E., Fixed points for set valued functions without continuity (1998) Indian J. Pure Appl. Math., 29, pp. 227-238
  • Jungck, G., Sessa, S., Fixed point theorems in best approximation theory (1995) Math. Jap., 42, pp. 249-252
  • Kamran, T., Coincidence and fixed points for hybrid strict contractions (2004) J. Math. Anal. Appl., 299, pp. 235-241
  • Kamran, T., Multivalued f-weakly Picard mappings (2007) Nonlinear Anal., 67, pp. 2289-2296
  • Kaneko, H., Sessa, S., Fixed point theorems for compatible multivalued and single valued mappings (1989) Int. J. Math. Math. Sci., 12, pp....
  • Khan, A.R., Akbar, F., Sultana, N., Hussain, N., Coincidence and invariant approximation theorems for generalized f-nonexpansive multivalued...
  • Kuratowski, K., Ryll-Nardzewski, C., A general theorem on selectors (1965) Bull. Acad. Polon. Sci. Ser. Sci. Math. Astron. Phys., 13, pp....
  • Latif, A., Bano, A., A result on invariant approximation (2002) Tamkang J. Math., 33, pp. 89-92
  • Latif, A., Tweddle, I., On multivalued nonexpansive maps (1999) Demo. Math., 32, pp. 565-574
  • Nadlar Jr., S.B., Multivalued contraction mappings (1969) Pacific J. Math., 30, pp. 475-488
  • Rhaodes, B.E., On multivalued f-nonexpansive maps (2001) Fixed Point Theory Appl., 2, pp. 89-92
  • Sahab, S.A., Khan, M.S., Sessa, S., A result in best approximation theory (1988) J. Approx. Theory, 55, pp. 349-351
  • Shahzad, N., Invariant approximation and R-subweakly commuting maps (2001) J. Math. Anal. Appl., 257, pp. 39-45
  • Shahzad, N., Some general random coincidence point theorems (2004) N. Z. J. Math., 33, pp. 95-103
  • Shahzad, N., Hussain, N., Deterministic and random coincidence point results for f-nonexpansive maps (2006) J. Math. Anal. Appl., 323, pp....