Research Article
BibTex RIS Cite

α-admissible contractions on quasi-metric-like space

Year 2017, Volume: 1 Issue: 2, 113 - 124, 20.12.2017
https://doi.org/10.31197/atnaa.379092

Abstract

In the setting of a complete quasi-metric-like spaces we investigate some fixed point problems via admissible mappings. Contractive condition includes (c)-comparison function. Definition of (α,ψ)-contraction is generalized and continuity of f is replaced with regularity of observed space. Presented results improve and extend several results on quasi-metric-like spaces.

References

  • T. Abedeljawad, E. Karapınar and K. Taş, Existence and uniqueness of common fixed point on partial metric spaces, Appl. Math. Lett. 24 (2011) 1894–1899.
  • A. Amini-Harandi, Metric-like spaces, partial metric spaces and xed points, Fixed Point Theory Appl. (2012), 2012:204
  • H. Aydi, E. Karapnar and W. Shatanawi, Coupled xed point results for ( ; ')-weakly contractive condition in ordered partial metric spaces, Comput. Math. Appl. 62 (2011) 4449-4460.
  • H. Aydi, E. Karapinar and C. Vetro, On Ekeland's variational principle in partial metric spaces, Appl. Math. Inf. Sci. 9(2015), 257-262.
  • I.A. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal., Unianowsk Gos. Ped. Inst. 30(1989), 26-37.
  • V. Berinde, Une generalization de critere du dAlembert pour les series positives, Bul. St. Univ. Baia Mare, 7 (1991), 21-26.
  • V. Berinde, Generalized contractions in quasimetric spaces, Seminar on Fixed Point Theory, Preprint 3 (1993), 3-9.
  • V. Berinde, Contractii generalizate si aplicatii , Editura Cub Press 22, Baia Mare, Romania
  • V. Berinde, Sequences of operators and xed points in quasimetric spaces, Stud. Univ. Babes-Bolyai Math., 16(4) (1996), 23-27.
  • N. Bourbaki, Topologie generale, Herman, Paris, 1974.
  • M. Cvetkovic, E. Karapinar and V. Rakocevic, Some xed point results on quasi-b-metric like spaces, J. Inequal. Appl., 2015 (2015), 2015:374
  • Lj. Ciric, B. Samet, H. Aydi and C. Vetro, Common xed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comput. 218 (2011), 2398-2406.
  • P. Hitzler and A.K. Seda, Dislocated topologies. J. Electr. Eng. 51 (2000), 3-7.
  • E. Karapınar, P. Kuman and P. Salimi, On 􀀀 -Meir-Keeler contractive mappings, Fixed Point Theory Appl. (2013), 2013:94.
  • E. Karapınar and P. Salimi, Dislocated metric space to metric spaces with some xed point theorems, Fixed Point Theory Appl (2013), 2013:222
  • E. Karapınar and B. Samet, Generalized ( 􀀀 ) contractive type mappings and related xed point theorems with applications, Abstr. Appl. Anal 2012 (2012), Article ID: 793486
  • S. G. Matthews, Metric Domains for Completeness, Ph.D. Thesis, Research Report, Dept. Comput. Sci., University of Warwick 76 (1986)
  • S. G. Matthews, The Topology of Partial Metric Spaces, Research Report RR222 (1992), University of Warwick
  • S. G. Matthews, Partial metric spaces, Ann. New York Acad. Sci. 728 (1994), 183-197.
  • S. J. O'Neill, Partial metrics, valuations, and domain theory, Papers on general topology and applications, Gorham, ME, (1995), 304-315.
  • O. Popescu, Some new xed point theorems for -Geraghty contraction type maps in metric spaces, Fixed Point Theory Appl. (2014), 2014:190
  • J.J.M.M. Rutten, Elements of Generalized Ultrametric Domain Theory, Theoretic. Comput. Sci. 170 (1996), 349-381.
  • B. Samet, C. Vetro and P. Vetro, 􀀀 -contractive type mappings, Nonlinear Anal. 75 (2012), 2154-2165.
  • I. R. Sarma and P. S. Kumari, On dislocated metric spaces. Int. J. Math. Arch. 3 (2012), 72-77.
  • R. Shrivastava, Z. K. Ansari and M. Sharma, Some results on xed points in dislocated and dislocated quasi-metric spaces, J. Adv. Stud. Topol. 3 (2012), 25-31.
  • F. M. Zeyada, G. H. Hassan, and M. A. Ahmed. A generalization of a xed point theorem due to Hitzler and Seda in dislocated quasi-metric spaces. The Arabian J. for Sci. and Eng., 31 (2005), 111-114.
  • K. Zoto, E. Hoxha and A. Isufati, Some new results in dislocated and dislocated quasi-metric spaces, Appl. Math. Sci. 71 (2012), 3519-3526.
Year 2017, Volume: 1 Issue: 2, 113 - 124, 20.12.2017
https://doi.org/10.31197/atnaa.379092

Abstract

References

  • T. Abedeljawad, E. Karapınar and K. Taş, Existence and uniqueness of common fixed point on partial metric spaces, Appl. Math. Lett. 24 (2011) 1894–1899.
  • A. Amini-Harandi, Metric-like spaces, partial metric spaces and xed points, Fixed Point Theory Appl. (2012), 2012:204
  • H. Aydi, E. Karapnar and W. Shatanawi, Coupled xed point results for ( ; ')-weakly contractive condition in ordered partial metric spaces, Comput. Math. Appl. 62 (2011) 4449-4460.
  • H. Aydi, E. Karapinar and C. Vetro, On Ekeland's variational principle in partial metric spaces, Appl. Math. Inf. Sci. 9(2015), 257-262.
  • I.A. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal., Unianowsk Gos. Ped. Inst. 30(1989), 26-37.
  • V. Berinde, Une generalization de critere du dAlembert pour les series positives, Bul. St. Univ. Baia Mare, 7 (1991), 21-26.
  • V. Berinde, Generalized contractions in quasimetric spaces, Seminar on Fixed Point Theory, Preprint 3 (1993), 3-9.
  • V. Berinde, Contractii generalizate si aplicatii , Editura Cub Press 22, Baia Mare, Romania
  • V. Berinde, Sequences of operators and xed points in quasimetric spaces, Stud. Univ. Babes-Bolyai Math., 16(4) (1996), 23-27.
  • N. Bourbaki, Topologie generale, Herman, Paris, 1974.
  • M. Cvetkovic, E. Karapinar and V. Rakocevic, Some xed point results on quasi-b-metric like spaces, J. Inequal. Appl., 2015 (2015), 2015:374
  • Lj. Ciric, B. Samet, H. Aydi and C. Vetro, Common xed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comput. 218 (2011), 2398-2406.
  • P. Hitzler and A.K. Seda, Dislocated topologies. J. Electr. Eng. 51 (2000), 3-7.
  • E. Karapınar, P. Kuman and P. Salimi, On 􀀀 -Meir-Keeler contractive mappings, Fixed Point Theory Appl. (2013), 2013:94.
  • E. Karapınar and P. Salimi, Dislocated metric space to metric spaces with some xed point theorems, Fixed Point Theory Appl (2013), 2013:222
  • E. Karapınar and B. Samet, Generalized ( 􀀀 ) contractive type mappings and related xed point theorems with applications, Abstr. Appl. Anal 2012 (2012), Article ID: 793486
  • S. G. Matthews, Metric Domains for Completeness, Ph.D. Thesis, Research Report, Dept. Comput. Sci., University of Warwick 76 (1986)
  • S. G. Matthews, The Topology of Partial Metric Spaces, Research Report RR222 (1992), University of Warwick
  • S. G. Matthews, Partial metric spaces, Ann. New York Acad. Sci. 728 (1994), 183-197.
  • S. J. O'Neill, Partial metrics, valuations, and domain theory, Papers on general topology and applications, Gorham, ME, (1995), 304-315.
  • O. Popescu, Some new xed point theorems for -Geraghty contraction type maps in metric spaces, Fixed Point Theory Appl. (2014), 2014:190
  • J.J.M.M. Rutten, Elements of Generalized Ultrametric Domain Theory, Theoretic. Comput. Sci. 170 (1996), 349-381.
  • B. Samet, C. Vetro and P. Vetro, 􀀀 -contractive type mappings, Nonlinear Anal. 75 (2012), 2154-2165.
  • I. R. Sarma and P. S. Kumari, On dislocated metric spaces. Int. J. Math. Arch. 3 (2012), 72-77.
  • R. Shrivastava, Z. K. Ansari and M. Sharma, Some results on xed points in dislocated and dislocated quasi-metric spaces, J. Adv. Stud. Topol. 3 (2012), 25-31.
  • F. M. Zeyada, G. H. Hassan, and M. A. Ahmed. A generalization of a xed point theorem due to Hitzler and Seda in dislocated quasi-metric spaces. The Arabian J. for Sci. and Eng., 31 (2005), 111-114.
  • K. Zoto, E. Hoxha and A. Isufati, Some new results in dislocated and dislocated quasi-metric spaces, Appl. Math. Sci. 71 (2012), 3519-3526.
There are 27 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Marija Cvetkovic This is me

Vladimir Rakocevic

Publication Date December 20, 2017
Published in Issue Year 2017 Volume: 1 Issue: 2

Cite