Geodesic
Generalized contractions to coupled fixed point theorems in partially ordered metric spaces
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 4, pp. 492-502.

Voir la notice de l'article provenant de la source Math-Net.Ru

The purpose of this paper is to establish some coupled fixed point theorems for a self mapping satisfying certain rational type contractions along with strict mixed monotone property in a metric space endowed with partial order. Also, we have given the result of existence and uniqueness of a coupled fixed point for the mapping. This result generalize and extend several well known results in the literature.
Keywords: partially ordered metric spaces, rational contractions, coupled fixed point, monotone property. 
@article{JSFU_2020_13_4_a10,
     author = {N. Seshagiri Rao and Karusala Kalyani},
     title = {Generalized contractions to coupled fixed point theorems in partially ordered metric spaces},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {492--502},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2020_13_4_a10/}
}
TY  - JOUR
AU  - N. Seshagiri Rao
AU  - Karusala Kalyani
TI  - Generalized contractions to coupled fixed point theorems in partially ordered metric spaces
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2020
SP  - 492
EP  - 502
VL  - 13
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2020_13_4_a10/
LA  - en
ID  - JSFU_2020_13_4_a10
ER  - 
%0 Journal Article
%A N. Seshagiri Rao
%A Karusala Kalyani
%T Generalized contractions to coupled fixed point theorems in partially ordered metric spaces
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2020
%P 492-502
%V 13
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2020_13_4_a10/
%G en
%F JSFU_2020_13_4_a10
N. Seshagiri Rao; Karusala Kalyani. Generalized contractions to coupled fixed point theorems in partially ordered metric spaces. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 4, pp. 492-502. http://geodesic.mathdoc.fr/item/JSFU_2020_13_4_a10/

[1] S. Banach, “Sur les operations dans les ensembles abstraits et leur application aux equations untegrales”, Fund. Math., 3 (1922), 133–181

[2] B.K. Dass, S. Gupta, “An extension of Banach contraction principle through rational expression”, Indian Journal of Pure and Applied Mathematics, 6 (1975), 1455–1458

[3] S.K. Chetterjee, “Fixed point theorems”, C.R. Acad. Bulgara Sci., 25 (1972), 727–730

[4] M. Edelstein, “On fixed points and periodic points under contraction mappings”, J. Lond. Math. Soc., 37 (1962), 74–79

[5] G.C. Hardy, T. Rogers, “A generalization of fixed point theorem of S. Reich”, Can. Math. Bull., 16 (1973), 201–206

[6] D.S. Jaggi, “Some unique fixed point theorems”, Indian J. Pure Appl. Math., 8 (1977), 223–230

[7] R. Kannan, “Some results on fixed points-II”, Am. Math. Mon., 76 (1969), 71–76

[8] S. Reich, “Some remarks concerning contraction mappings”, Can. Math. Bull., 14 (1971), 121–124

[9] M.R. Singh, A.K. Chatterjee, “Fixed point theorems”, Commun. Fac. Sci. Univ. Ank. Series A1, 37 (1988), 1–4

[10] D.R. Smart, Fixed Point Theorems, Cambridge University Press, Cambridge, 1974

[11] C.S. Wong, “Common fixed points of two mappings”, Pac. J. Math., 48 (1973), 299–312

[12] R.P. Agarwal, M.A. El-Gebeily, D. O'Regan, “Generalized contractions in partially ordered metric spaces”, Appl. Anal., 87 (2008), 1–8

[13] I. Altun, B. Damjanovic, D. Djoric, “Fixed point and common fixed point theorems on ordered cone metric spaces”, Appl. Math. Lett., 23 (2010), 310–316

[14] A. Amini-Harandi, H. Emami, “A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations”, Nonlinear Analysis: Theory, Methods $\$ Applications, 72 (2010), 2238–2242

[15] M. Arshad, A. Azam, P. Vetro, “Some common fixed results in cone metric spaces”, Fixed Point Theory Appl., 2009 (2009), 493965

[16] M. Arshad, J. Ahmad, E. Karapinar, “Some common fixed point results in rectangular metric spaces”, Int. J. Anal., 2013 (2013), 307234

[17] T.G. Bhaskar, V. Lakshmikantham, “Fixed point theory in partially ordered metric spaces and applications”, Nonlinear Analysis: Theory, Methods $\$ Applications, 65 (2006), 1379–1393

[18] S. Hong, “Fixed points of multivalued operators in ordered metric spaces with applications”, Nonlinear Analysis: Theory, Methods $\$ Applications, 72 (2010), 3929–3942

[19] J.J. Nieto, R.R. Lopez, “Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations”, Order, 22 (2005), 223–239

[20] J.J. Nieto, R.R. Lopez, “Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equation”, Acta Math. Sin. Engl. Ser., 23:12 (2007), 2205–2212

[21] M. Ozturk, M. Basarir, “On some common fixed point theorems with rational expressions on cone metric spaces over a Banach algebra”, Hacet. J. Math. Stat., 41:2 (2012), 211–222

[22] A.C.M. Ran, M.C.B. Reurings, “A fixed point theorem in partially ordered sets and some application to matrix equations”, Proc. Am. Math. Soc., 132 (2004), 1435–1443

[23] E.S. Wolk, “Continuous convergence in partially ordered sets”, Gen. Topol. Appl., 5 (1975), 221–234

[24] X. Zhang, “Fixed point theorems of multivalued monotone mappings in ordered metric spaces”, Appl. Math. Lett., 23 (2010), 235–240

[25] H. Aydi, E. Karapinar, W. Shatanawi, “Coupled fixed point results for $(\psi, \varphi)$-weakly contractive condition in ordered partial metric spaces”, Comput. Math. Appl., 62:12 (2011), 4449–4460

[26] V. Berinde, “Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces”, Nonlinear Analysis: Theory, Methods and Applications, 74:18 (2011), 7347–7355

[27] V. Berinde, “Coupled fixed point theorems for $F$-contractive mixed monotone mappings in partially ordered metric spaces”, Nonlinear Analysis: Theory, Methods and Applications, 75:6 (2012), 3218–3228

[28] V. Berinde, M. Pacurar, “Coupled and triple fixed point theorems for mixed monotone almost contractive mappings in partially ordered metric spaces”, Journal of Nonlinear and Convex Analysis, 18:4 (2017), 651–659

[29] B.S. Choudhury, A. Kundu, “A coupled coincidence point result in partially ordered metric spaces for compatible mappings”, Nonlinear Analysis: Theory, Methods $\$ Applications, 73 (2010), 2524–2531

[30] L. Ciric, M.O. Olatinwo, D. Gopal, G. Akinbo, “Coupled point theorems for mappings satisfying a contractive condition of rational type on a partially ordered metric space”, Adv. Fixed Point Theory, 2 (2012), 1–8

[31] E. Karapinar, “Couple fixed point on cone metric spaces”, Gazi Univ. J. Sci., 24:1 (2011), 51–58

[32] V. Lakshmikantham, L.B. Ciric, “Couple fixed point theorems for nonlinear contractions in partially ordered metric spaces”, Nonlinear Analysis: Theory, Methods $\$ Applications, 70 (2009), 4341–4349

[33] N.V. Luong, N.X. Thuan, “Coupled fixed points in partially ordered metric spaces and application”, Nonlinear Analysis: Theory, Methods $\$ Applications, 74 (2011), 983–992

[34] A. Petrusel, G. Petrusel, Discrete Dynamics in Nature and Society, 2015 (2015), 143510 | DOI

[35] A. Petrusel, G. Petrusel, J.C. Yao, “Contributions to the coupled coincidence point problem in b-metric spaces with applications”, FILOMAT, 31:10 (2017), 3173–3180

[36] A. Petrusel, G. Petrusel, J.C. Yao, “Coupled fixed points theorems in quasi metric spaces without mixed monotonicity”, Carpathian J. Math., 35:2 (2019), 169–176

[37] B. Samet, “Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces”, Nonlinear Anal., 74:12 (2010), 4508–4517

[38] S. Chandok, T.D. Narang, M.A. Taoudi, “Some coupled fixed point theorems for mappings satisfying a generalized contractive condition of rational type”, Palestine Journal of Mathematics, 4:2 (2015), 360–366

[39] C. Vetro, H.K. Nashine, B. Samet, “Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces”, Mathematical and Computer Modelling, 54 (2011), 712–720

[40] C. Vetro, B. Samet, “Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces”, Nonlinear Analysis, 74 (2011), 4260–4268

[41] C. Vetro, “Coupled coincidence points for compatible mappings satisfying mixed monotone property”, The Journal of Nonlinear Sciences and its Applications, 5 (2012), 104–114

[42] C. Vetro, “Coupled common fixed point theorems in partially ordered G-metric spaces for nonlinear contractions”, Mathematica Moravica, 18 (2014), 45–62