We obtain (common) fixed point results for mappings in b-metric and b-rectangular metric spaces, under the Pata-type conditions. In particular, we show that the results of paper Balasubramanian, [S. Balasubramanian, Math. Sci. (Springer) 8 (2014), no. 3, 65-69] can be obtained as consequences of more general results and in a much shorter way. We demonstrate these facts by some examples.
Keywords: b-metric space, b-rectangular metric space, Pata-type condition.
Kadelburg, Zoran  1 ; Radenović, Stojan  2
@article{10_22436_jnsa_008_06_05,
author = {Kadelburg, Zoran and Radenovi\'c, Stojan},
title = {Pata-type common fixed point results in b-metric and b-rectangular metric spaces},
journal = {Journal of nonlinear sciences and its applications},
pages = {944-954},
year = {2015},
volume = {8},
number = {6},
doi = {10.22436/jnsa.008.06.05},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.06.05/}
}
TY - JOUR AU - Kadelburg, Zoran AU - Radenović, Stojan TI - Pata-type common fixed point results in b-metric and b-rectangular metric spaces JO - Journal of nonlinear sciences and its applications PY - 2015 SP - 944 EP - 954 VL - 8 IS - 6 UR - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.06.05/ DO - 10.22436/jnsa.008.06.05 LA - en ID - 10_22436_jnsa_008_06_05 ER -
%0 Journal Article %A Kadelburg, Zoran %A Radenović, Stojan %T Pata-type common fixed point results in b-metric and b-rectangular metric spaces %J Journal of nonlinear sciences and its applications %D 2015 %P 944-954 %V 8 %N 6 %U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.06.05/ %R 10.22436/jnsa.008.06.05 %G en %F 10_22436_jnsa_008_06_05
Kadelburg, Zoran; Radenović, Stojan. Pata-type common fixed point results in b-metric and b-rectangular metric spaces. Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 6, p. 944-954. doi: 10.22436/jnsa.008.06.05
[1] Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, Volume 64 (2014), pp. 941-960
[2] Fixed point theory for quasi-contraction maps in b-metric spaces, Fixed Point Theory, Volume 15 (2014), pp. 351-358
[3] Multivalued fixed point theorems in cone b-metric spaces, J. Inequal. Appl., Volume 2013 (2013), pp. 1-9
[4] The contraction mapping principle in quasi-metric spaces [in Russian], Funk. An. Ulianowsk Gos. Ped. Inst., Volume 30 (1989), pp. 26-37
[5] A Pata-type fixed point theorem, Math. Sci., Volume 8 (2014), pp. 65-69
[6] A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, Volume 57 (2000), pp. 31-37
[7] A fixed point theorem for Kannan-type maps in metric spaces, arXiv (2012), pp. 1-7
[8] A generalization of Banach's contraction principle , Proc. Amer. Math. Soc., Volume 45 (1974), pp. 267-273
[9] Some Recent Results in Metrical Fixed Point Theory, Faculty of Mechanical Engineering, University of Belgrade, Belgrade, 2003
[10] Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, Volume 1 (1993), pp. 5-11
[11] Common fixed points in generalized metric spaces, Appl. Math. Comput., Volume 218 (2012), pp. 7322-7325
[12] Pata contractions and coupled type fixed points, Fixed Point Theory Appl., Volume 2014 (2014), pp. 1-10
[13] Rectangular b-metric spaces and contraction principle, J. Nonlinear Sci. Appl. (in press)
[14] Common fixed point results for \(\psi-\varphi\) contractions in rectangular metric spaces, Bull. Math. Anal. Appl., Volume 5 (2013), pp. 44-52
[15] Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., Volume 332 (2007), pp. 1468-1476
[16] Suzuki-type fixed point results in metric type spaces, Fixed Point Theory Appl., Volume 2012 (2012), pp. 1-12
[17] Fixed points of cyclic (\(\psi-\varphi, L, A,B\))-contractive mappings in ordered b-metric spaces with applications, Fixed Point Theory Appl., Volume 2013 (2013), pp. 1-18
[18] Common fixed point results in metric type spaces, Fixed Point Theory Appl., Volume 2010 (2010), pp. 1-15
[19] Common fixed points for noncontinuous nonself maps on nonmetric spaces, Far East J. Math. Sci., Volume 4 (1996), pp. 199-215
[20] Fixed point and tripled fixed point theorems under Pata-type conditions in ordered metric space, Intern. J. Anal. Appl., Volume 6 (2014), pp. 113-122
[21] Fixed point results in generalized metric spaces without Hausdorff property, Math. Sci., Volume 8 (2014), pp. 1-8
[22] On generalized metric spaces: a survey, TWMS J. Pure Appl. Math., Volume 5 (2014), pp. 3-13
[23] Fixed point theorems for Pata-type maps in metric spaces, J. Egypt. Math.Soc. (in press)
[24] A note on Pata-type cyclic contractions, Sarajevo J. Math. (in press)
[25] A note on b-cone metric and its related results: Generalizations or equivalence?, Fixed Point Theory Appl., Volume 2013 (2013), pp. 1-7
[26] Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl., Volume 2010 (2010), pp. 1-7
[27] KKM mappings in metric type spaces, Nonlinear Anal., Volume 73 (2010), pp. 3123-3129
[28] Fixed Point Theory in Distance Spaces, Springer, cham, 2014
[29] Some equivalences between cone b-metric spaces and b-metric spaces, Abstract Appl. Anal., Volume 2013 (2013), pp. 1-8
[30] Fixed point of a Ljubomir Ćirić's quasi-contraction mapping in generalized metric spaces, Publ. Math. Debrecen, Volume 61 (2002), pp. 589-594
[31] Common fixed points of \(\alpha-\psi-\varphi\)-contractions in generalized metric spaces, Nonlinear Anal. Model. Control, Volume 19 (2014), pp. 43-54
[32] A fixed point theorem in metric spaces, J. Fixed Point Theory Appl., Volume 10 (2011), pp. 299-305
[33] Fixed point results to tvs-cone b-metric spaces, Gulf J. Math., Volume 1 (2013), pp. 51-64
[34] New fixed point results in b-generalized metric spaces , Nonlinear Anal. Model. Control. (submitted)
[35] Quasi-contractions on symmetric and cone symmetric spaces, Banach J. Math. Anal., Volume 5 (2011), pp. 38-50
[36] Some results on weak contraction maps, Bull. Iranian Math. Soc., Volume 38 (2012), pp. 625-645
[37] Common fixed point theorems for weakly isotone increasing mappings in ordered b-metric spaces, J. Nonlinear Sci. Appl., Volume 7 (2014), pp. 229-245
[38] Discussion on `A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces' by A. Branciari , Publ. Math. Debrecen , Volume 76 (2010), pp. 493-494
[39] Contractions over generalized metric spaces , J. Nonlinear Sci. Appl., Volume 2 (2009), pp. 180-182
[40] A generalized Banach fixed point theorem, Bull. Malasiyan Math. Sci. Soc. (in press)
[41] Generalized metric spaces do not have the compatible topology, Abstract Appl. Anal., Volume 2014 (2014), pp. 1-5
[42] Various generalizations of metric spaces and fixed point theorems, Rev. Real Acad. Cienc. Exac., Fis. Nat., Ser. A, Math., Volume 109 (2015), pp. 175-198
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