BibTex RIS Cite

FIXED POINT THEOREMS FOR GENERALIZED ; ' -WEAK CONTRACTIONS

Year 2017, Volume: 7 Issue: 2, 261 - 271, 01.12.2017

Abstract

In this paper, we prove some xed point theorems for generalized ; ' - weak contractive mappings in a metric space. Our result generalized and extend recent results of Singh et al.[16, Theorem 2.1], Doric [7, Theorem 2.1], Rhoades [15, Theorem 1] and Dutta and Choudhary [9, Theorem 2.1]. Also, we provid an example to support the useability of our results.

References

  • Banach,B., (1922), Surles operations dons les ensembles abstraits et leur application aux equations integrales, Fundamenta Mathematicae., 3, pp.133-181.
  • Bilgili,N., Karapinar,E. and Turkoglu,D., (2013), A note on common fixed points for (psi,alpha,beta)- weakly contractive mappings in generalized metric spaces, Fixed Point Theory and Applications., doi: 1186/1687-1812-2013-287.
  • Chauhan,S., Karapinar,E., Shatanawi,W., and Vetro,C., (2015), Fixed points of weakly compatible mappings satisfying generalized ϕ-weak contractions, Bulletin of the Malaysian Mathematical Sciences Society., 38, pp.1085-1105.
  • Chi,K.P., Karapinar,E. and Thanh,T.D., (2013), On the fixed point theorems in generalized weakly contractive mappings on partial metric spaces Bulletin of the Iranian Mathematical Society, 39, pp.369
  • ´Ciri´c,L.B., (1974) A generalization of Banachs contraction principle, Proc. Amer. Math. Soc., 45, pp.267-273.
  • ´Ciri´c,L.B., (1972), Fixed points for generalized multivalued contractions, Mat. Vesnik., 9, pp.265-272.
  • Dori´c,D., (2009), Common fixed point for generalized (ψ −ϕ)-weak contractions, Applied Mathematics Letters., 22, pp.1896-1900.
  • Dung,N.V. and Hang,V.T.L, (2015), A fixed point theorem for generalized F-contractions on complete metric spaces.Vietnam Journal of Mathematics., doi: 10.1007/s10013-015-0123-5.
  • Dutta,P.N. and Choudhary, B.S., (2008), A generalization of contraction principle in metric spaces,Fixed Point Theory Appl., doi: 10.1155/2008/406368.
  • Karapinar,E., (2012), Weak φ-contraction on partial contraction, J. Comput. Anal. Appl., 14, pp.206
  • Karapinar,E. and Rakocevic,V., (2013), On cyclic generalized weakly C-contractions on partial metric spaces, Abstract and Applied Analysis., http://dx.doi.org/10.1155/2013/831491.
  • Karapinar, E. and Sadarangani, K., (2013), Triple Fixed Point Theorems For Weak (psi-phi)
  • Contractions, J. Comput. Anal. Appl., 15, pp. 844-851. Karapinar,E. and Shatanawi,W., (2012), On weakly (C,psi,phi)-contractive mappings in partiallly ordered metric spaces Abstr. Appl. Anal., http://dx.doi.org/10.1155/2012/495892.
  • Kinces,J. and Totik,V., (1990), Theorems and counter examples on contractive mappings, Math. Balkanica., 4, pp.69-90.
  • Rhoades,B.E., (2001), Some theorems on weakly contractive maps, Nonlinear Anal. 47, pp.2683-2693.
  • Singha,S.L., Kamalb,R., Senc,M.D.l. and Chughb,R., (2015), A Fixed Point Theorem for Generalized Weak Contractions, Filomat., 29, pp.1481-1490.
  • Suzuki,T., (2009), A new type of fixed point theorem in metric spaces , Nonlinear Analysis. 71, pp.5313-5317.
  • W lodarczyk,K. and Plebaniak,P., (2011), Kannan-type contractions and fixed points in uniform spaces, Fixed Point Theory and Applications., doi: 10.1186/1687-1812-2011-90.
  • W lodarczyk,K. and Plebaniak,R., (2012), Contractivity of Leader type and fixed points in uni- formspaces with generalized pseudodistances, Journal of Mathematical Analysis and Applications., , pp.533-541.
Year 2017, Volume: 7 Issue: 2, 261 - 271, 01.12.2017

Abstract

References

  • Banach,B., (1922), Surles operations dons les ensembles abstraits et leur application aux equations integrales, Fundamenta Mathematicae., 3, pp.133-181.
  • Bilgili,N., Karapinar,E. and Turkoglu,D., (2013), A note on common fixed points for (psi,alpha,beta)- weakly contractive mappings in generalized metric spaces, Fixed Point Theory and Applications., doi: 1186/1687-1812-2013-287.
  • Chauhan,S., Karapinar,E., Shatanawi,W., and Vetro,C., (2015), Fixed points of weakly compatible mappings satisfying generalized ϕ-weak contractions, Bulletin of the Malaysian Mathematical Sciences Society., 38, pp.1085-1105.
  • Chi,K.P., Karapinar,E. and Thanh,T.D., (2013), On the fixed point theorems in generalized weakly contractive mappings on partial metric spaces Bulletin of the Iranian Mathematical Society, 39, pp.369
  • ´Ciri´c,L.B., (1974) A generalization of Banachs contraction principle, Proc. Amer. Math. Soc., 45, pp.267-273.
  • ´Ciri´c,L.B., (1972), Fixed points for generalized multivalued contractions, Mat. Vesnik., 9, pp.265-272.
  • Dori´c,D., (2009), Common fixed point for generalized (ψ −ϕ)-weak contractions, Applied Mathematics Letters., 22, pp.1896-1900.
  • Dung,N.V. and Hang,V.T.L, (2015), A fixed point theorem for generalized F-contractions on complete metric spaces.Vietnam Journal of Mathematics., doi: 10.1007/s10013-015-0123-5.
  • Dutta,P.N. and Choudhary, B.S., (2008), A generalization of contraction principle in metric spaces,Fixed Point Theory Appl., doi: 10.1155/2008/406368.
  • Karapinar,E., (2012), Weak φ-contraction on partial contraction, J. Comput. Anal. Appl., 14, pp.206
  • Karapinar,E. and Rakocevic,V., (2013), On cyclic generalized weakly C-contractions on partial metric spaces, Abstract and Applied Analysis., http://dx.doi.org/10.1155/2013/831491.
  • Karapinar, E. and Sadarangani, K., (2013), Triple Fixed Point Theorems For Weak (psi-phi)
  • Contractions, J. Comput. Anal. Appl., 15, pp. 844-851. Karapinar,E. and Shatanawi,W., (2012), On weakly (C,psi,phi)-contractive mappings in partiallly ordered metric spaces Abstr. Appl. Anal., http://dx.doi.org/10.1155/2012/495892.
  • Kinces,J. and Totik,V., (1990), Theorems and counter examples on contractive mappings, Math. Balkanica., 4, pp.69-90.
  • Rhoades,B.E., (2001), Some theorems on weakly contractive maps, Nonlinear Anal. 47, pp.2683-2693.
  • Singha,S.L., Kamalb,R., Senc,M.D.l. and Chughb,R., (2015), A Fixed Point Theorem for Generalized Weak Contractions, Filomat., 29, pp.1481-1490.
  • Suzuki,T., (2009), A new type of fixed point theorem in metric spaces , Nonlinear Analysis. 71, pp.5313-5317.
  • W lodarczyk,K. and Plebaniak,P., (2011), Kannan-type contractions and fixed points in uniform spaces, Fixed Point Theory and Applications., doi: 10.1186/1687-1812-2011-90.
  • W lodarczyk,K. and Plebaniak,R., (2012), Contractivity of Leader type and fixed points in uni- formspaces with generalized pseudodistances, Journal of Mathematical Analysis and Applications., , pp.533-541.
There are 19 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

H. Pırı This is me

S. Rahrovı This is me

Publication Date December 1, 2017
Published in Issue Year 2017 Volume: 7 Issue: 2

Cite