Geodesic
Coincidence point results and its applications in partially ordered metric spaces
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 3, pp. 397-407.

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The purpose of this paper is to establish some common fixed point theorems for $f$-nondecreasing self-mapping satisfying a certain rational type contraction condition in the frame of a metric spaces endowed with partial order. Also, some consequences of the results in terms of an integral type contractions are presented in the space. Further, the monotone iterative technique has been used to find a unique solution of an integral equation.
Keywords: ordered metric space, rational contraction, compatible mappings, coincidence point, common fixed point. 
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N. Seshagiri Rao; Karusala Kalyani; Tekle Gemechu. Coincidence point results and its applications in partially ordered metric spaces. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 3, pp. 397-407. http://geodesic.mathdoc.fr/item/JSFU_2022_15_3_a12/

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

[2] B.K. Dass, S. Gupta, “An extension of Banach contraction principle through rational expression”, Indian J. Pure Appl. Math., 6 (1975), 1455–1458 | MR | Zbl

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

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

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

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

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

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

[9] P.L. Sharma, A.K. Yuel, “A unique fixed point theorem in metric space”, Bull. Cal. Math. Soc., 76 (1984), 153–156 | MR | Zbl

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

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

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

[13] 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 Anal., Theory Methods Appl., 72 (2010), 2238–2242 | DOI | MR | Zbl

[14] C. Ankush, B. Damjanovic, D. Lakshmi Kanta, “Fixed point results on metric spaces via simulation functions”, Filomat, 31:11 (2017), 3365–3375 | DOI | MR | Zbl

[15] J. Harjani, B. Lopez, K. Sadarangani, “A fixed point theorem for mappings satisfying a contractive condition of rational type on a partially ordered metric space”, Abstr. Appl. Anal., 2010 (2010), 190701, 8 pp. | DOI | MR | Zbl

[16] S. Hong, “Fixed points of multivalued operators in ordered metric spaces with applications”, Nonlinear Anal., Theory Methods Appl., 72 (2010), 3929–3942 | DOI | MR | Zbl

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

[18] J.J. Nieto, “An abstract monotone iterative technique”, Nonlinear Analysis, Theory Methods and Applications, 28:12 (1997), 1923–1933 | DOI | MR | Zbl

[19] 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 | DOI | MR | Zbl

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

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

[22] T.G. Bhaskar, V. Lakshmikantham, “Fixed point theory in partially ordered metric spaces and applications”, Nonlinear Anal., Theory Methods Appl., 65 (2006), 1379–1393 | DOI | MR | Zbl

[23] V. Lakshmikantham, L.J.Ćirić, “Coupled fixed point theorems for nonlinear contractions in partially ordered metric space”, Nonlinear Anal., 70 (2009), 4341–4349 | DOI | MR | Zbl

[24] M. Arshad, A. Azam, P. Vetro, “Some common fixed results in cone metric spaces”, Fixed Point Theory Appl., 2009, 493965 | DOI | MR | Zbl

[25] M. Arshad, J. Ahmad, E. Karapinar, “Some common fixed point results in rectangular metric spaces”, Int. J. Anal., 2013, 307234 | MR | Zbl

[26] 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 | DOI | MR | Zbl

[27] Y.J. Cho, M.H. Shah, N. Hussain, “Coupled fixed points of weakly $F$-contractive mappings in topological spaces”, Appl. Math. Lett., 24 (2011), 1185–1190 | DOI | MR | Zbl

[28] L.J.Ćirić, N. Cakić, M Rajović, J.S. Ume, “Monotone generalized nonlinear contractions in partially ordered metric spaces”, Fixed Point Theory Appl., 2008, no. 11, 131294 | MR

[29] S. Chandok, “Some common fixed point results for generalized weak contractive mappings in partially ordered metrix spaces”, Journal of Nonlinear Anal. Opt., 4 (2013), 45–52 | MR | Zbl

[30] S. Chandok, “Some common fixed point results for rational type contraction mappings in partially ordered metric spaces”, Mathematica Bohemica, 138:4 (2013), 407–413 | DOI | MR | Zbl

[31] E. Graily, S.M. Vaezpour, R. Saadati, Y.J. Cho, “Generalization of fixed point theorems in ordered metric spaces concerning generalized distance”, Fixed Point Theory Appl., 2011, 30 | DOI | MR | Zbl

[32] E. Karapinar, “Couple fixed point theorems for nonlinear contractions in cone metric spaces”, Comput. Math. Appl., 59:12 (2010), 3656–3668 | DOI | MR | Zbl

[33] 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 | MR | Zbl

[34] F. Sabetghadam, H.P. Masiha, A.H. Sanatpour, “Some coupled fixed point theorems in cone metric spaces”, Fixed point Theory Appl., 2009, no. 8, 125426 | MR | Zbl

[35] B. Samet, H. Yazidi, “Coupled fixed point theorems in partially ordered $\epsilon$-chainable metric spaces”, J. Math. Comput. Sci., 1 (2010), 142–151 | DOI | MR

[36] W. Shatanawi, “Partially ordered cone metric spaces and coupled fixed point results”, Comput. Math. Appl., 60 (2010), 2508–2515 | DOI | MR | Zbl

[37] W. Sintunavarat, Y.J. Cho, P. Kumam, “Common fixed point theorems for $c$-distance in ordered cone metric space”, Comput. Math. Appl., 62 (2011), 1969–1978 | DOI | MR | Zbl

[38] N. Seshagiri Rao, K. Kalyani, “Generalized Contractions to Coupled Fixed Point Theorems in Partially Ordered Metric Spaces”, Journal of Siberian Federal University. Mathematics $\$ Physics, 13:4 (2020), 492–502 | DOI | MR | Zbl

[39] N. Seshagiri Rao, K. Kalyani, “Coupled fixed point theorems with rational expressions in partially ordered metric spaces”, The Journal of Analysis, 28:4 (2020), 1085–1095 | DOI | MR | Zbl

[40] N. Seshagiri Rao, K. Kalyani, Kejal Khatri, “Contractive mapping theorems in Partially ordered metric spaces”, CUBO, 22:2 (2020), 203–214 | DOI | MR | Zbl

[41] N. Seshagiri Rao, K. Kalyani, “Unique fixed point theorems in partially ordered metric spaces”, Heliyon, 6:11 (2020), e05563 | DOI | MR

[42] N. Seshagiri Rao, K. Kalyani, “Generalized fixed point results of rational type contractions in partially ordered metric spaces”, BMC Research Notes, 14:390 (2021), 13 pp. | DOI | MR

[43] K. Kalyani, N. Seshagiri Rao, Belay Mituku, “On fixed point theorems of monotone functions in Ordered metric spaces”, The Journal of Analysis, 2021, 14 pp. | DOI | MR

[44] E. Liz, J.J. Nieto, “Periodic boundary value problem for integro-differentail equations with general kernel”, Dynamical Systems and Applications, 3 (1994), 297–304 | MR | Zbl