Fixed Point Theorems for Occasionally Weakly Compatible Mappings in Dislocated-Metric Spaces

Kastriot Zoto^1, , Elida Hoxha² and Panda Sumati Kumari³

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

²Department of Mathematics, Faculty of Natural Sciences, University of Tirana; Tirana, Albania

³KL University, Green Fields, Vaddeswaram, Guntur District, Andhra Pradesh, India

Cite this paper:
Kastriot Zoto, Elida Hoxha and Panda Sumati Kumari. Fixed Point Theorems for Occasionally Weakly Compatible Mappings in Dislocated-Metric Spaces. Turkish Journal of Analysis and Number Theory. 2014; 2(2):37-41. doi: 10.12691/tjant-2-2-2

Abstract

In this paper we prove some fixed point theorems for one and two pairs of selfmaps which are occasionally weakly compatible and satisfy a “max” and contractive conditions. Also, some existing results are derived as corollaries from theorems of this paper in the framework of dislocated metric spaces.

Keywords:
occasionally weakly compatible dislocated metric contraction condition common fixed point

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References:

[1]	M. Aamri and D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl., 270 (2002), 181-188.
[2]	M.A. Al-Thagafi and N. Shahzad, Generalized I-nonexpansive selfmaps and invariant approximations, Acta Math. Sinica, 24(5) (2008), 867-876.
[3]	A. Bhatt, H. Chandra and D.R. Sahu, Common fixed point theorems for occasionally weakly compatible mappings under relaxed conditions, Nonlinear Analysis, 73(1) (2010), 176-182.
[4]	H. Chandra and A. Bhatt, Fixed point theorems for occasionally weakly compatible maps in probabilistic semi-metric space, Int. J. Math. Anal., 3(12) (2009), 563-570.
[5]	S. Chauhan and B. D. Pant, Common fixed point theorems for occasionally weakly compatible mappings using implicit relation, Journal of the Indian Math. Soc., 77(1-4) (2010) 13-21.
[6]	I. Beg, M. Abbas, Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition, Fixed Point Theory and Applications, 2006, Article ID 74503, pages 1-7.
[7]	S. S. Chauhan and K. Utreja, A common fixed point theorem in dislocated metric space, International Journal of Engineering and Innovative Technology (IJEIT), vol 3. Issue1. July 2013.
[8]	M. Abbas and B. E. Rhoades, Common fixed point theorems for occasionally weakly compatible mappings satisfying a generalized contractive condition Mathematical Communications 13(2008), 295-301 295.
[9]	G. Jungck, B. E. Rhoades, Fixed point theorems for occasionally weakly compatible mappings, Fixed Point Theory 7(2006), 287-296.
[10]	G. Jungck, B. E. Rhoades, Fixed point theorems for occasionally weakly compatible mappings, Fixed Point Theory 9(2008), 383-384 (erratum).
[11]	K. Zoto and E. Hoxha, Fixed point theorems in dislocated and dislocated quasi-metric spaces.Journal of advanced study in topology vol4.nr.3, 2012.
[12]	A. Isufati. Fixed point theorems in dislocated quasi-metric space. Appl. Math. Sci., 4(5): 217-223, 2010.
[13]	Kumari et al, Common fixed point theorems on weakly compatible maps on dislocated metric spaces. Mathematical Sciences 2012 6:71.
[14]	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.
[15]	K. Zoto, Weakly compatible mappings and fixed points in dislocated -metric spaces, International journal of mathematical archive, vol. 4 (6), 2013, 131-137.
[16]	K. Jha and D. Panthi, A Common Fixed Point Theorem in Dislocated Metric Space, Appl. Math. Sci., vol. 6, 2012, no. 91, 4497-4503.
[17]	K. P. R. Rao and P. Rangaswamy, Common Fixed Point Theorem for Four Mappings in Dislocated Quasi-Metric Space, The Nepali Math. Sci. Report, 30 (1-2), 2010, 70-75.
[18]	P. Hitzler and A. K. Seda. Dislocated topologies. J. Electr. Engin., 51(12/S): 3: 7, 2000.
[19]	P. Hitzler: Generalized metrics and topology in logic programming semantics, Ph. D Thesis, School of Mathematics, Applied Mathematics and Statistics, National University Ireland, University college Cork, 2001.
[20]	R. Shrivastava, Z.K. Ansari and M. Sharma. Some results on Fixed Points in Dislocated and Dislocated Quasi-Metric Spaces. Journal of Advanced Studies in Topology; Vol. 3, No.1, 2012,
[21]	I. R. Sarma and P. S. Kumari, “On dislocated metric spaces,” International Journal of Mathematical Archive, vol. 3, no. 1, pp. 72-77, 2012.
[22]	Hussain et al, Common fixed point results for weak contractive mappings in ordered b-dislocated metric spaces with applications. Journal of Inequalities and Applications 2013, 2013: 486.
[23]	P. S. Kumari, Some fixed point theorems in generalized dislocated metric spaces, Mathematical Theory and Modeling, 1 (4), 16-22.