Fixed point theorems for α-Geraghty contraction type maps in generalized metric spaces

K. P. R. Sastry, G.V.R. Babu, P.S. kumar, B. Ramu Naidu

Abstract


In this paper, we extend the notion of α-Geraghty contraction type maps on metric space to generalized metric spaces and we obtain conditions for α-Geraghty contraction on a generalized metric space to have a fixed point. We also establish the corresponding result in generalized metric spaces with partial order. Examples are provided to illustrate and highlight the results.


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References


A. C. M. Ran and M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132(5),1435-1443(2004).

A. Hamini-Harandi, H. Emami: A fixed point theorem for contraction type maps in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal, 72, 2238-2242 (2010).

B. Samet, C. Vetro, p. Vetro , Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Analysis. 75(2012)2154-2165.

C. T. Aage and J. N. Salunke, The results on fixed points in dislocated and dislocated quasi-metric space,Appl.Maths.Sci.2(59), 2941-948(2008).

E. Karapinar, P. Kumam and P. Salimi, On α-ψ- Meirr-Keeler contractive mappings, Fixed Point Theory Appl. 2013, 94(2013).

E. Karapinar and P. Salimi dislocated metric space to metric spaces with some fixed point theorems. Fixed point theory and Appl. 2013, 222(2013).

J. J. Nieto and R. Rodriguez-Lopez, Contractive mapping theorem in partially ordered sets and applications to ordinary differential equations. Order 22, (2005), 223-239.

K. P. R. Sastry, G. Appalanaidu, Ch. Srinivasa Rao and B. Ramunaidu: Fixed point theorems for weak k-quasi contractions on a generalized metric space, Bulletin of Mathematics and Statistics Research, vol.4.s1.2016, ISSN:2348-0580.

L. B. Ciric, A generalization of Banach’s contraction principle. Proc.Amer.Math.Soc, 45(2), 267-273(1974).

M. Geraghty, On contractive mappings, Proc.Amer.Maths.Soc.40 (1973)604-608.

M. Jleli and B. Samet, A generalized metric space and related fixed point theorems ,Fixed point theory and Applications, (2015)2015:61 DOI:10:1186-S1 3663-015-0312-7.

M. A. Ahmed, F. M. Zeyada and G. F. Hasan, Fixed point theorems in generalized types of dislocated metric spaces and its applications, Thai.J.Math,11,67-73(2013).

P. Hitzler, Generalized metrics and topology in logical programming

semantics.Dissertation,Faculty of Science,National university of Ireland, University College,Cork(2000).

P. Hitzler and A. K. Seda, Dislocated topologies.J.Electr.Eng.51(2),3-7(2000).

S. Czerwik, Contraction mappings in b-metric spaces, Acia .Math.Inform.Univ.Ostrav,1, 5-11(1993).

S. H. Cho, J. S. Bae and E. Karapinar, Fixed point theorems for - Geraghty contraction type maps in metric spaces , Fixed Point Theory and Appl. 2013, 2013:329.

W. Kirk and N. Shahzad, b-metric spaces, Fixed Point Theory in Distance Spaces, pp113-131, Springer, Berlin(2014).


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