International Journal of Nonlinear Analysis and Applications

Some contraction fixed point theorems in partially ordered modular metric spaces

Document Type : Research Paper

Author

Department of Mathematics, Payame Noor University, Tehran, Iran

Abstract

In this paper, we prove some fixed point theorems for modular metric spaces endowed with partial order sets by using the mixed monotone mapping property which is a generalization of the definitions and results of T. Gnana Bhaskar and V. Lakshmikantham.

Keywords

[1] R.P. Agarwal, M.A. El-Gebbeily and D. Oregan, Generalized contractions in partially ordered metric spaces, Appl. Anal. 87 (2008), no. 1, 109–116.
[2] A. Amini-Harandi and H. Emami, A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equation, Nonlinear Anal. 72 (2010), no. 5, 2238–2242.
[3] S. Banach, sur les operations dans les ensembles abstraits et leur applications aux ´equations integral, Fund. Math. 3 (1992), 133–181.
[4] P. Chaipunya, C. Mongkolkeha, W. Sintunavarat and P. Kumam, Fixed point theorems for multivalued mappings in modular metric spaces, Abstr. Appl. Anal. 2012 (2012), 1–14.
[5] V.V. Chystyakov, Modular metric spaces generated by F-modulars, Folia Math. 15 (2008), no. 1, 3–24.
[6] V.V. Chystyakov, Modular metric spaces I: Basic concepts, Nonlinear Anal. 72 (2010), no. 1, 1–14.
[7] V.V. Chystyakov, Modular metric spaces II: Application to superposition operators, Nonlinear Anal. 72 (2010), no. 1, 15–30.
[8] V.V. Chystyakov, A fixed point theorem for contractions in modular metric spaces, arXiv preprint arXiv:1112.5561 (2011).
[9] T. Gnana Bhaskar and V. Lakshmikantham, Fixed point theorem in partially ordered metric space with applications, Nonlinear Anal. 65 (2006), no. 7, 1379–1393.
[10] K. Goebd and W.A. Kirk, Topics in metric fixed point theory, Cambridge Studies in Advanced Mathematics, 28. Cambridge University Press, Cambridge, 1990.
[11] J. Harjani and K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal. 72 (2010), no. 3-4, 1188–1197.
[12] M.A. Khamsi, W.M. Kozlowski and S. Reich, Fixed point theory in modular function spaces, Nonlinear Anal. 14 (1990), no. 11, 935–953.
[13] C. Mongkolkeha, W. Sintunavarat and P. Kumam, Fixed point theorem for contraction mappings in modular metric spaces, Fixed Point Theory Algorithms Sci. Eng. 2011 (2011), no. 93, 1–9.
[14] J. Musielak and W. Orlicz, On modular spaces, Studia Math. 18 (1959), 49–65.
[15] H. Nakano, Modular semi-ordered spaces, Maruzen Co., Ltd., Tokyo, 1950.
[16] J.J. Nieto and R. Lopez, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta. Math. Sin. English Ser. 23 (2007), 2205–2212.
[17] H. Rahimpoor, A. Ebadian, M. Eshaghi Gordji and A. Zohri, Fixed point theory for generalized quasi-contraction maps in modular metric spaces, J. Math. Comput. Sci. 10 (2014), no. 1, 54–60.
[18] H. Rahimpoor, A. Ebadian, M. Eshaghi Gordji and A. Zohri, Some fixed point theorems on modular metric spaces, Acta Univ. Apulensis 37 (2014), no. 37, 161–170.
International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 9
September 2023
Pages 273-282
  • Receive Date: 17 November 2021
  • Revise Date: 11 December 2021
  • Accept Date: 26 December 2021