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A Related Fixed Point Theorem for $F$-Contractions on Two Metric Spaces

Year 2019, Volume: 48 Issue: 1, 150 - 156, 01.02.2019

Abstract

Recently, Wardowski in [Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012] introduced the concept of $F$-contraction on complete metric space which is a proper generalization of Banach contraction principle. In the present paper, we proved a related fixed point theorem with $F$-contraction mappings on two complete metric spaces.

References

  • A. Aliouche and B. Fisher, A related fixed point theorem for two pairs of mappings on two complete metric spaces, Hacet. J. Math. Stat. 34, 39-45, 2005.
  • I. Altun, G. Durmaz, G. Mınak and S. Romaguera, Multivalued almost $F$-contractions on complete metric spaces, Filomat 30 (2), 441-448, 2016.
  • B. Fisher, Fixed points on two metric spaces, Glas. Mat. Ser. III 16 (36), 333-337, 1981.
  • B. Fisher, Related fixed points on two metric spaces, Math. Sem. Notes Kobe Univ. 10, 17-26, 1982.
  • B. Fisher, R.K. Jain and H.K. Sahu, Related fixed point theorems for three metric spaces, Novi Sad J. Math. 26 (1), 11-17, 1996.
  • M. Imdad, R. Gubran, M. Arif and D. Gopal, An observation on $\alpha$-type $F$-contractions and some ordered-theoretic fixed point results, Math. Sci. 11 (3), 247-255, 2017.
  • G. Mınak, A. Helvacı and I. Altun, Ciric type generalized $F$-contractions on complete metric spaces and fixed point results, Filomat 28 (6), 1143-1151, 2014.
  • G. Mınak, M. Olgun and I. Altun, A new approach to fixed point theorems for multivalued contractive maps, Carpathian J. Math. 31 (2), 241-248, 2015.
  • R.K. Namdeo, D. Gupta and B. Fisher, A related fixed point theorem on two metric spaces, Punjab Univ. J. Math. 27, 109-112, 1994.
  • R.K. Namdeo, S. Jain and B. Fisher, A related fixed point theorem for two pairs of mappings on two complete metric spaces, Hacet. J. Math. Stat. 32, 7-11, 2013.
  • M. Olgun, G. Mınak and I. Altun, A new approach to Mizoguchi-Takahashi type fixed point theorems, J. Nonlinear Convex Anal. 17 (3), 579-587, 2016.
  • H. Piri and P. Kumam, Some fixed point theorems concerning $F$-contraction in complete metric spaces, Fixed Point Theory Appl. 2014, 210, 2014.
  • M. Sgrio and C. Vetro, Multi-valued $F$-contractions and the solution of certain functional and integral equations, Filomat 27 (7), 1259-1268, 2013.
  • D. Singh, V. Joshi, M. Imdad and P. Kumam, Fixed point theorems via generalized $F$-contractions with applications to functional equations occurring in dynamic programming, J. Fixed Point Theory Appl. 19 (2), 1453-1479, 2017.
  • F. Vetro, F-contractions of Hardy-Rrogers type and application to multistage decision processes, Nonlinear Anal. Model. Control 21 (4), 531-546, 2016.
  • D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012, 94, 2012.
  • D.Wardowski and N.V. Dung, Fixed points of $F$-weak contractions on complete metric spaces, Demonstratio Math. 47 (1), 146-155, 2014.
Year 2019, Volume: 48 Issue: 1, 150 - 156, 01.02.2019

Abstract

References

  • A. Aliouche and B. Fisher, A related fixed point theorem for two pairs of mappings on two complete metric spaces, Hacet. J. Math. Stat. 34, 39-45, 2005.
  • I. Altun, G. Durmaz, G. Mınak and S. Romaguera, Multivalued almost $F$-contractions on complete metric spaces, Filomat 30 (2), 441-448, 2016.
  • B. Fisher, Fixed points on two metric spaces, Glas. Mat. Ser. III 16 (36), 333-337, 1981.
  • B. Fisher, Related fixed points on two metric spaces, Math. Sem. Notes Kobe Univ. 10, 17-26, 1982.
  • B. Fisher, R.K. Jain and H.K. Sahu, Related fixed point theorems for three metric spaces, Novi Sad J. Math. 26 (1), 11-17, 1996.
  • M. Imdad, R. Gubran, M. Arif and D. Gopal, An observation on $\alpha$-type $F$-contractions and some ordered-theoretic fixed point results, Math. Sci. 11 (3), 247-255, 2017.
  • G. Mınak, A. Helvacı and I. Altun, Ciric type generalized $F$-contractions on complete metric spaces and fixed point results, Filomat 28 (6), 1143-1151, 2014.
  • G. Mınak, M. Olgun and I. Altun, A new approach to fixed point theorems for multivalued contractive maps, Carpathian J. Math. 31 (2), 241-248, 2015.
  • R.K. Namdeo, D. Gupta and B. Fisher, A related fixed point theorem on two metric spaces, Punjab Univ. J. Math. 27, 109-112, 1994.
  • R.K. Namdeo, S. Jain and B. Fisher, A related fixed point theorem for two pairs of mappings on two complete metric spaces, Hacet. J. Math. Stat. 32, 7-11, 2013.
  • M. Olgun, G. Mınak and I. Altun, A new approach to Mizoguchi-Takahashi type fixed point theorems, J. Nonlinear Convex Anal. 17 (3), 579-587, 2016.
  • H. Piri and P. Kumam, Some fixed point theorems concerning $F$-contraction in complete metric spaces, Fixed Point Theory Appl. 2014, 210, 2014.
  • M. Sgrio and C. Vetro, Multi-valued $F$-contractions and the solution of certain functional and integral equations, Filomat 27 (7), 1259-1268, 2013.
  • D. Singh, V. Joshi, M. Imdad and P. Kumam, Fixed point theorems via generalized $F$-contractions with applications to functional equations occurring in dynamic programming, J. Fixed Point Theory Appl. 19 (2), 1453-1479, 2017.
  • F. Vetro, F-contractions of Hardy-Rrogers type and application to multistage decision processes, Nonlinear Anal. Model. Control 21 (4), 531-546, 2016.
  • D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012, 94, 2012.
  • D.Wardowski and N.V. Dung, Fixed points of $F$-weak contractions on complete metric spaces, Demonstratio Math. 47 (1), 146-155, 2014.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Murat Olgun

Özge Biçer

Tuğçe Alyıldız This is me

İshak Altun

Publication Date February 1, 2019
Published in Issue Year 2019 Volume: 48 Issue: 1

Cite

APA Olgun, M., Biçer, Ö., Alyıldız, T., Altun, İ. (2019). A Related Fixed Point Theorem for $F$-Contractions on Two Metric Spaces. Hacettepe Journal of Mathematics and Statistics, 48(1), 150-156.
AMA Olgun M, Biçer Ö, Alyıldız T, Altun İ. A Related Fixed Point Theorem for $F$-Contractions on Two Metric Spaces. Hacettepe Journal of Mathematics and Statistics. February 2019;48(1):150-156.
Chicago Olgun, Murat, Özge Biçer, Tuğçe Alyıldız, and İshak Altun. “A Related Fixed Point Theorem for $F$-Contractions on Two Metric Spaces”. Hacettepe Journal of Mathematics and Statistics 48, no. 1 (February 2019): 150-56.
EndNote Olgun M, Biçer Ö, Alyıldız T, Altun İ (February 1, 2019) A Related Fixed Point Theorem for $F$-Contractions on Two Metric Spaces. Hacettepe Journal of Mathematics and Statistics 48 1 150–156.
IEEE M. Olgun, Ö. Biçer, T. Alyıldız, and İ. Altun, “A Related Fixed Point Theorem for $F$-Contractions on Two Metric Spaces”, Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 1, pp. 150–156, 2019.
ISNAD Olgun, Murat et al. “A Related Fixed Point Theorem for $F$-Contractions on Two Metric Spaces”. Hacettepe Journal of Mathematics and Statistics 48/1 (February 2019), 150-156.
JAMA Olgun M, Biçer Ö, Alyıldız T, Altun İ. A Related Fixed Point Theorem for $F$-Contractions on Two Metric Spaces. Hacettepe Journal of Mathematics and Statistics. 2019;48:150–156.
MLA Olgun, Murat et al. “A Related Fixed Point Theorem for $F$-Contractions on Two Metric Spaces”. Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 1, 2019, pp. 150-6.
Vancouver Olgun M, Biçer Ö, Alyıldız T, Altun İ. A Related Fixed Point Theorem for $F$-Contractions on Two Metric Spaces. Hacettepe Journal of Mathematics and Statistics. 2019;48(1):150-6.