Strength of dynamic technique to rational type contraction in partially ordered metric spaces and extension of out comes of coupled fixed point

Subject Areas : Fixed point theory

S. K.  Tiwari ¹ (Department of Mathematics, Dr. C. V. Raman University, Kota, Bilaspur-495001, Chhattisgarh, India)
J. P.  Ganvir ² (Department of Mathematics, Dr. C. V. Raman University, Kota, Bilaspur-495001, Chhattisgarh, India)

Received: 2023-02-06 Accepted : 2023-03-31 Published : 2023-03-31

Keywords:

References:

[1] R. P. Agrawal, M. A. El-Gebeily, D. O’regan, Generalized contractions in partially ordered metric spaces, Appl. Anal. 87 (2008), 1-8.

[2] I. Altun, H. Simsek, Some fixed point theorem on ordered metric spaces and application. Fixed Point Theory Appl. (2010), 2020:621469.

[3] A. Amini Harandi, H. Emami, A fixed point theorem for contraction type maps in partially ordered metric spaces, Appl. Math. Lett. 23 (2010), 310-316.

[4] H. Aydi, E. Karpinar, W. Shantanwi, Coupled fixed point results for (ψ,φ) weakly contractive conditions in ordered partial metric spaces, Comput. Math. Appl. 62 (12) (2011), 4449-4460.

[5] S. Banach, Sur les operations dans les ensembles abstraits et leur applications aux equations integrals, Fund. Math. 3 (1922), 133-181.

[6] T. G. Bhaskar, V. Laxmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), 1379-1393.

[7] S. Chandok, T. D. Narang, M. A. Taudi, Some coupled fixed point theorems for mappings satisfying a generalized contractive conditions of rational type, Palestin J. Math. 4 (2) (2015), 360-366.

[8] B. S. Choudhary, A. Kundu, A coupled coincidence point results in partially ordered metric spaces for campatiable mappings, Nonlinear Anal. 73 (2010), 2524-2531.

[9] L. B. Ciric, B. Damjanovic, M. Jleli, B. Samet, Coupled fixed point theorem for generalized Mizoguchi-Takahashi contractions with applications, Fixed point Theory Appl. (2012), 2012:51.

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

[11] J. Harjani, K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal. 72 (3-4) (2010), 1188-1197.

[12] E. Karapinar, Coupled fixed point theorem for nonlinear contractions type maps in cone metric spaces, Comput. Math. Appl. 59 (12) (2010), 3656-3668.

[13] E. Karapinar, Coupled fixed point theorem on cone metric spaces, Gazi Uni. J. Sci. 24 (1) (2011), 51-58.

[14] P. Kumam, F. Rouzcard, M. Imdad, D. Gopal, Fixed point theorems on ordered metric space through a rational contraction, Abstr. Appl. Anal. (2013), 2013:206515.

[15] V. Lakshmikantham, L. B. Ciric, Coupled Fixed point theorem for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70 (2009), 4341-4349.

[16] N. V. Luong, N. X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74 (2011), 983-992.

[17] B. Monjadet, Metrics on artially ordered sets-A survey, Discreat Math. 35 (1-3) (1981), 173-184.

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

[19] J. J. Nieto, R. R. Lopez, Existance and uniqueness of fixed point in partially ordered sets and applications, Acta. Math. Sin. Engl. Ser. 23 (12) (2007), 2205-2212.

[20] J. J. Nieto, L. Pouso, R. R. Lopez, Fixed point theorems in ordered abstract spaces, Proc. Amer. Math. Soc. 135 (2007), 2505-2517.

[21] H. Rahimi, S. Radenovic, G. Soleimani Rad, P. Kumam, Quadrupled fixed point results in abstract metric spaces, Comp. Appl. Math. 33 (2014), 671-685.

[22] H. Rahimi, P. Vetro, G. Soleimani Rad, Coupled fixed point results for T-contractions cone metric spaces with applications, Math. Notes. 98 (2015), 158-167.

[23] A. C. M. Ran, M. C. B. Reuring, A fixed point theorem in partially ordered sets and some application to metrix equations, Proc. Amer. Math. Soc. 132 (2004), 1435-1443.

[24] N. S. Rao, K. Kalyani, Coupled fixed point theorems in partially ordered metric space, Fasciculi Mathematici. 64 (2020), 77-89.

[25] B. Samet, Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric space, Comput. Math. Appl. 62 (12) (2011), 4508-4517.

[26] M. R. Singh, A. K. Chatterjee, Fixed point theorems, Commu. Fac. Sci. Univ. Ank. Ser. 37 (1988), 1-4.

[27] S. E. Wolk, Continuous convergence in partially ordered sets, Gen. Topol. Appl. 5 (1975), 221-234.

[28] M. Zhou, I. Xiao Liu, D. Dolicanin-Dekic, B. Damjanovic, Coupled coincidence point results for Geraghty type contraction by using monotone property in partially ordered S-metric spaces, J. Nonliner Sci. Appl. 9 (12) (2016), 5950-5969.