American Journal of Numerical Analysis
ISSN (Print): 2372-2118 ISSN (Online): 2372-2126 Website: http://www.sciepub.com/journal/ajna Editor-in-chief: Emanuele Galligani
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American Journal of Numerical Analysis. 2014, 2(3), 79-84
DOI: 10.12691/ajna-2-3-3
Open AccessArticle

Some Fixed Point Theorems and Cyclic Contractions in Dislocated and Dislocated Quasi-Metric Spaces

Kastriot Zoto1, , Panda Sumati Kumari2 and Elida Hoxha3

1Department of Mathematics and Computer Sciences, Faculty of Natural Sciences, University of Gjirokastra, Gjirokastra, Albania

2KL University, Green Fields, Vaddeswaram, Guntur District, Andhra Pradesh, India

3Department of Mathematics, Faculty of Natural Sciences, University of Tirana, Albania

Pub. Date: March 23, 2014

Cite this paper:
Kastriot Zoto, Panda Sumati Kumari and Elida Hoxha. Some Fixed Point Theorems and Cyclic Contractions in Dislocated and Dislocated Quasi-Metric Spaces. American Journal of Numerical Analysis. 2014; 2(3):79-84. doi: 10.12691/ajna-2-3-3

Abstract

In this paper, we established some common fixed point theorems for types of cyclic contractions in the setting of dislocated metric spaces. Using type of contraction introduced by Geraghty [19] and a class of continuous functions G3 in [10] we extend, generalize and unify some results in the existing literature.

Keywords:
cyclic map cyclical contraction dislocated metric common fixed point

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References:

[1]  A. A Eldered and P Veeramani (2006) Convergence and existence for Best proximity Points. J. Math Analysis and Applications, 323, 1001-1006.
 
[2]  C. T. Aage and J. N. Salunke. The results on fixed points in dislocated and dislocated quasi-metric space. Appl. Math. Sci., 2(59): 2941-2948, 2008.
 
[3]  C. T. Aage and J. N. Salunke Some results of fixed point theorem in dislocated quasi-metric spaces, Bulletin of Marathwada Mathematical Society, 9(2008), 1-5.
 
[4]  Erdal Karapinar and Inci M Erhan (2010) Best Proximity on Different Type Contractions Applied Mathematics and Information Science
 
[5]  E. Karapinar and H. K. Nashine (2013) Fixed point Theorems for Kannan type cyclic weakly contractions Journal of Nonlinear Analysis and Optimization, vol. 4, N0. 1, (2013), 29-35.
 
[6]  E. Karapinar, Fixed point Ttheory for cyclic weak φ -contraction, Appl. Math. Lett. 24 (2011) 822-825.
 
[7]  E. Karapinar and P. Salimi, Dislocated metric space to metric spaces with some fixed point theorems, Fixed point theory and applications (2013).
 
[8]  G Petrushel (2005), Cyclic representations and Periodic points, Studia Univ. Babes - Bloyai Math, 50, 107-112.
 
[9]  K. Jha and D. Panthi, A Common Fixed Point Theorem in Dislocated Metric Space, Appl. Math. Sci., vol. 6, 2012, no. 91, 4497-4503.
 
[10]  K. Zoto and E. Hoxha Fixed point theorems in dislocated and dislocated quasi-metric space Journal of Advanced Studies in Topology; Vol. 3, No.1, 2012.
 
[11]  K. Zoto and Hoxha, E: Fixed point theorems for cyclic contractions. Proceedings in ARSA, the second conference of advanced research in scientific areas. 2-6 december2013.
 
[12]  P. Hitzler and A. K. Seda. Dislocated topologies. J. Electr. Engin., 51(12/S):3:7, 2000.
 
[13]  P. Hitzler. Generalized Metrics and Topology in Logic Programming Semantics. Ph.d. thesis, National University of Ireland,University College Cork, 2001.
 
[14]  Pacurar M., Rus, I.A - (2010) Fixed Point Theory for φ -contractions, Nonlinear Anlaysis, 72, (3-4), 1181-1187.
 
[15]  Reny George, R. Rajagopalan, S. Vinayagam;Cyclic contractions and fixed points in dislocated metric spaces. Int. Journal of Math. Analysis, vol. 7, 2013, no.9, 403-411.
 
[16]  S. Karpagam and Sushma Agrawal (2010) Best Proximity Points theorems for Cyclic Meir Keeler Contraction Maps.
 
[17]  Sh.Rezapur and M.Derafshpour and N.Shahzad - Best Proximity point of cyclic φ contractions in ordered metric spaces Topological Methods in Nonlinear Analysis (in press).
 
[18]  W.A.Kirk and P.S. Srinivasan and P.Veeramani(2003) Fixed Points for mapping satsifying Cyclic contractive conditions. Fixed Point Theory, 4, 79-89.
 
[19]  M. A. Geraghty, On contractive mappings, Proc. Amer. Math. Soc. 40(1973), 604-608.
 
[20]  F. M. Zeyada, G. H. Hasan and M. A. Ahmed, A generalization of a fixed point theorem due to Hitzler and Seda in dislocated quasi-metric spaces, Arab. J. Sci. Eng. Sec. A Sci. 31(1) (2006) 111-114.