New Geraghty type contractions on metric-like spaces

Very recently, Fulga and Proca [A. Fulga, A. M. Proca, Abstr. Appl. Anal., (In press)] considered new Geraghty type contraction mappings and established a fixed point theorem for such mappings in complete metric spaces. In this paper, we prove the analogous result in the class of metric-like spaces which generalizes the main result of Karapinar et al. [E. Karapınar, H. H. Alsulami, M. Noorwali, Fixed Point Theory Appl., 2015 (2015), 22 pages]. We give some examples illustrating the presented result where [E. Karapınar, H. H. Alsulami, M. Noorwali, Fixed Point Theory Appl., 2015 (2015), 22 pages] is not applicable. An application is also provided. c ©2017 All rights reserved.

[1]  R. Shrivastava,et al.  Some Results on Fixed Points in Dislocated and Dislocated Quasi-Metric Spaces , 2012 .

[2]  Common fixed point theorems on weakly compatible maps on dislocated metric spaces , 2012 .

[3]  E. Karapınar,et al.  Fixed Points of Modified -Contractive Mappings in Complete Metric-Like Spaces , 2015 .

[4]  E. Karapınar,et al.  A Generalized Meir-Keeler-Type Contraction on Partial Metric Spaces , 2012 .

[5]  V. Rakocević,et al.  Fixed Point Results for Various -Admissible Contractive Mappings on Metric-Like Spaces , 2014 .

[6]  Vahid Parvaneh,et al.  Fixed Points of Contractive Mappings in b-Metric-Like Spaces , 2014, TheScientificWorldJournal.

[7]  A. Fulga,et al.  Fixed points for φE-Geraghty contractions , 2017 .

[8]  Dislocated Topologies 1 , 2000 .

[9]  Z. Kastriot.  SOME NEW RESULTS IN DISLOCATED AND DISLOCATED QUASI-METRIC SPACES , 2012 .

[10]  H. Aydi,et al.  Fixed points of multivalued nonself almost contractions in metric-like spaces , 2015 .

[11]  Some fixed point theorems in dislocated metric spaces , 2014 .

[13]  R. J. Hussain,et al.  in Dislocated Metric Spaces , 2012 .

[14]  C. T. Aage,et al.  The Results on Fixed Points in Dislocated and Dislocated Quasi-Metric Space , 2008 .

[15]  Some extensions for Geragthy type contractive mappings , 2015 .

[16]  Wasfi Shatanawi,et al.  Fixed and common fixed point theorems in partially ordered quasi-metric spaces , 2016 .

[17]  ERDAL KARAPINAR,et al.  FIXED POINT RESULTS FOR GENERALIZED α-ψ-CONTRACTIONS IN METRIC-LIKE SPACES AND APPLICATIONS , 2015 .

[18]  S. G. Matthews,et al.  Partial Metric Topology , 1994 .

[19]  A. Amini-Harandi,et al.  Metric-like spaces, partial metric spaces and fixed points , 2012, Fixed Point Theory and Applications.