Common Fixed Point Theorems for two Self-Mappings of a b-Metric Space Under an Implicit Relation  ABSTRACT  |  FULL TEXT 

Year 2011, Volume: 40 Issue: 6, 805 - 810, 01.06.2011

Mohamed Akkouchi

Keywords

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References

• Aamri, M. and El Moutawakil, D. Some new common fixed point theorems under strict contractive conditions, Math. Anal. Appl. 270, 181–188, 2002.
• Ali, J. and Imdad, M. An implicit function implies several contraction conditions Sarajevo J. Math. 4 (17), 269–285, 2008.
• Al-Thagafi, M. A. and Shahzad, N. Generalized I-nonexpansive selfmaps and invariant ap- proximations, Acta Mathematica Sinica, English Series, 24 (5), 867–876, 2008.
• Czerwik, S. Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis 1, 5–11, 1993.
• Czerwik, S. Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena, 46 (2) , 263–276, 1998.
• Imdad, M. and Khan, T. I. Fixed point theorems for some expansive mapping via implicit relations, Nonlinear Analysis Forum 9 (2), 209–218, 2004.
• Imdad, M. and Ali, J. Jungck’s common fixed point theorem and E.A Property, Acta Math- ematica Sinica, English Series 24 (1), 87–94, 2008.
• Jungck, G. Commuting mappings and fixed points, Amer. Math. Monthly 83, 261–263, 1976. [9] Jungck, G. Compatible mappings and common fixed points, Internat. J. Math. Math. Sci. 9, 771–779, 1986.
• Jungck, G. Common fixed points for noncontinuous nonself mappings on nonmetric spaces, Far. East, J. Math.Sci. 4, 199–215, 1996.
• Jungck, G. and Rhoades, B. E. Fixed point theorems for occasionally weakly compatible mappings, Fixed Point Theory 7 (2), 287–296, 2006.
• Pant, R. P. Common fixed points for non-commuting mappings, J. Math. Anal. Appl. 188, 436–440, 1994.
• Pant, R. P. Common fixed points of contractive maps J. Math. Anal. Appl. 226, 251–258, 1998.
• Pant, R. P. Common fixed points for mappings, Bull. Calcutta Math. Soc. 9, 281–287, 1998. [15] Pant, R. P. R-weak commutativity and common fixed points of noncompatible maps, Ganita 49(1), 19–27, 1998.
• Pant, R. P. R-weak commutativity and common fixed points, Soochow J. Math. 25, 37–42, 1999.
• Popa, V. Fixed point theorems for implicit contractive mappings, Stud. Cerc. St. Ser. Mat. Univ. Bacˇau 7 , 127–133, 1997.
• Popa, V. Some fixed point theorems for compatible mappings satisfying an implicit relation Demonstratio Math. 32, 157–163, 1999.
• Popa, V. A General fixed point theorem for expansive mappings under strict implicit con- ditions, Stud. Cerc. St. Ser. Mat. Univ. Bacˇau 17, 197–200, 2007.
• Popa, V. General fixed point theorems for occasionally weakly compatible mappings, Stud. Cerc. St. Ser. Mat. Univ. Bacˇau 17, Supplement, 193–200, 2007.
• Tiwari, R., Shrivastava, S. K. and Pathak, V. K. A common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying an integral type contractive condition, Hacet. J. Math. Stat. 39 (2), 151–158, 2010.