α-admissible contractions on quasi-metric-like space

Yıl 2017, , 113 - 124, 20.12.2017

Marija Cvetkovic Vladimir Rakocevic

https://doi.org/10.31197/atnaa.379092

Cited By: 1

Öz

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.

Anahtar Kelimeler

quasi-metric-like space, fixed point, α- admissible, (b)-comparison functions

Kaynakça

• 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.