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http://dx.doi.org/10.5831/HMJ.2016.38.2.213

STRICT COMMON FIXED POINT THEOREMS FOR HYBRID PAIRS OF MAPPINGS VIA ALTERING DISTANCES AND AN APPLICATION  

Ali, Javid (Department of Mathematics, Aligarh Muslim University)
Popa, Valeriu (Department of Mathematics, University of Bacau)
Imdad, Mohammad (Department of Mathematics, Aligarh Muslim University)
Publication Information
Honam Mathematical Journal / v.38, no.2, 2016 , pp. 213-229 More about this Journal
Abstract
In this paper, we utilize an implicit relation to improve and extend some strict common fixed point results of the existing literature to two pairs of hybrid mappings in 2-metric spaces via altering distances. As an application, we also prove some strict common fixed point theorems for hybrid pairs of mappings satisfying a contractive condition of integral type in 2-metric spaces.
Keywords
2-metric spaces; strict common fixed point; OWC hybrid mappings; altering distances and implicit relation;
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1 S. Gahler, 2-metrische Raume und ihre topologische structur, Math. Nachr. 26(1963), 115-148.   DOI
2 S. Gahler, Uber die Uniforisierbarkeit 2-metrischer Raume, Math. Nachr. 28(1965), 235-244.
3 S. Gahler, Zur Geometrie 2-metrischer Rume, Rev. Roumaine Math. Pures Appl. 11(1966), 665-667.
4 K. Iseki, Fixed point theorem in 2-metric spaces, Math. Sem. Notes Kobe Univ. 3(1)(1975), paper no. XIX, 4 pp.
5 K. Iseki, P. L. Sharma and B. K. Sharma, Contraction type mapping on 2-metric space, Math. Japon. 21(1976), 67-70.
6 G. Jungck, Common fixed points for noncontinuous nonself maps on nonmetric spaces, Far East J. Math. Sci. 4(1996), 199-215.
7 V. Popa, Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstratio Math. 32(1)(1999), 157-163.
8 M. Imdad, S. Kumar and M. S. Khan, Remarks on some fixed point theorems satisfying implicit relations, Rad. Mat. 11(2002), 135-143.
9 H. M. Abu-Donia and H. A. Atia, Common fixed points theorems in 2-metric spaces, preprint, 2007.
10 V. Popa, M. Imdad and J. Ali, Using implicit relations to prove unified fixed point theorems in metric and 2-metric spaces, Bull. Malays. Math. Sci. Soc. 33(2010), 105-120.
11 V. Popa, M. Imdad and J. Ali, Fixed point theorems for a class of mappings governed by strictly contractive implicit relations, Southeast Asian Bull. Math. 34(2010), 941-952.
12 M. S. Khan, M. Swaleh and S. Sessa, Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc. 30(1984), 1-9.   DOI
13 V. Popa and M. Mocanu, Altering distance and common fixed points under implicit relations, Hacet. J. Math. Stat. 38(2009), 329-337.
14 K. P. R. Sastry and G. V. R. Babu, Fixed point theorems in metric spaces by altering distances, Bull. Calcutta Math. Soc. 90(1998), 175-182.
15 M. D. Khan, A study of fixed point theorems, Ph.D. Thesis, Aligarh Muslim University, India, 1984.
16 K. P. R. Sastry and G. V. R. Babu, Some fixed point theorems by altering distances between the points, Indian J. Pure Appl. Math. 30(1999), 641-647.
17 P. P. Murthy, S. S. Chang, Y. J. Cho and B. K. Sharma, Compatible mappings of type (A) and common fixed point theorems, Kyungpook Math. J. 32(2)(1992), 203-216.
18 M. E. Abd El-Monsef, H. M. Abu-Donia and Kh. Abd-Rabou, New types of common fixed point theorems in 2-metric spaces, Chaos Solitons Fractals 41(2009), 1435-1441.   DOI
19 G. Jungck and B. E. Rhoades, Fixed points for set-valued functions without continuity, Indian J. Pure Appl. Math. 29(1998), 227-238.
20 M. Abbas and B. E. Rhoades, Common fixed point theorems for hybrid pairs of occasionally weakly compatible mappings, Pan Amer. Math. J. 18(2008), 56-62.
21 M. Imdad, J. Ali and V. Popa, Impact of occasionally weakly compatible property on common fixed point theorems for expansive mappings, Filomat 25(2011), 79-89.   DOI
22 D. Doric, Z. Kadelburg and S. Radenovic, A note on occasionally weakly compatible mappings and common fixed points, Fixed Point Theory 13(2012), 475-479.
23 H. Bouhadjera and C. Godet-Thobie, Common fixed point theorems for occasionally weakly compatible mappings, to appear.
24 M. Imdad, J. Ali and M. Tanveer, Remarks on some recent metrical common fixed point theorems, Appl. Math. Lett. 24(2011), 1165-1169.   DOI
25 A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Intern. J. Math. Math. Sci. 29(9)(2002), 531-536.   DOI
26 B. E. Rhoades, Two fixed point theorems for mappings satisfying a general contractive condition of integral type, Intern. J. Math. Math. Sci. 15(2005), 2359-2364.
27 A. Aliouche, A common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying a contractive condition of integral type, J. Math. Anal. Appl. 332(2006), 796-802.
28 S. Kumar, R. Chugh and R. Kumar, Fixed point theorem for compatible mappings satisfying a contractive condition of integral type, Soochow J. Math. 33(2)(2007), 181-185.
29 V. Popa and M. Mocanu, A new view point in the study of fixed points for mappings satisfying a contractive condition of integral type, Bull. Inst. Politeh. Iasi Sect. Mat. Mec. Teor. Fiz. 53(57), 5(2007), 269-272.
30 M. Mocanu and V. Popa, Some fixed point theorems for mappings satisfying implicit relations in symmetric spaces, Libertas Math. 28(2008), 1-13.