Theorems of Geraghty type generalized F-contraction for dislocated quasi-metric spaces
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Abstract
The generalized F-contraction, Geraghty contraction and admissible function are introduced as the most recent generalizations of the Banach contraction. The presence and uniqueness of fixed points for the newly constructed contraction’s self-mapping on complete metric spaces were investigated. The findings of this article can be interpreted as an improvement on the key findings of the previous article.
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References
Banach S. Sur les oprationes dans les ensembles abstraits et leur application aux équations intgrales. Fundam. Math. 1922;3:133-81.
Geraghty MA. On contractive mappings. Proc. Am. Math. Soc. 1973;40:604-8.
Samet B, Vetro C, Vetro P. Fixed point theorems for α–ψ-contractive type mappings. Nonlinear Anal. TMA. 2012;75(4):2154-65.
Chandok S. Some fixed point theorems for (α, β)-admissible Geraghty type contractive mappings and related results. Math. Sci. 2015;9(3):127-35.
Wardowski D. Fixed points of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl. 2012;2012:94.
Hitzler P. Generalized metrics and topology in logic programming semantics. Ph.D. thesis, National University of Ireland, University College Cork, 2001.
Zeyada F, Hassan G, Ahmed M. A generalization of a fixed point theorem due to Hitzler and Seda in dislocated quasi-metric spaces. Arab. J. Sci. Eng. 2005;31(1):111-4.
Popescu O. Some new fixed point theorems for α-Geraghty contraction type maps in metric spaces. Fixed Point Theory Appl. 2014;2014:190.
Cho S-H, Bae J-S, Karapınar E. Fixed point theorems for α-Geraghty contraction type maps in metric spaces. Fixed Point Theory Appl. 2013;2013:329.