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

Journal of Linear and Topological Algebra

دوره 12، شماره 01، خرداد 2023، صفحه 67-76   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.30495/jlta.2023.1981812.1546

نویسندگان

S. K. Tiwari^* ؛ J. P. Ganvir

Department of Mathematics, Dr. C. V. Raman University, Kota, Bilaspur-495001, Chhattisgarh, India

چکیده

We investigate the mechanisms of dynamic technique to rational type contraction in the context of partially ordered metric spaces and obtain coupled fixed points in this article. Our derived results extend and generalize some prominent outcomes in the literature. At last, we have produced an example and an application for a system of integral that preserve the main results.

کلیدواژه‌ها

Coupled fixed point؛ mixed monotone property, rational type contraction؛ partially ordered metric space

مراجع

[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.