Two extensions of coupled coincidence point results for nonlinear contractive mappings

Sedghi, Shaban; Kumam, Poom; Dosˇenovic´, Tatjana; Shobe, Nabi

doi:10.1016/j.joems.2014.06.002

Two extensions of coupled coincidence point results for nonlinear contractive mappings

Document Type : Original Article

Authors

¹ Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran

² Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bang Mod, Thung Khru, Bangkok 10140, Thailand

³ Faculty of Technology, Bulevar Cara Lazara 1, Novi Sad, Serbia

⁴ Department of Mathematics, Islamic Azad University-Babol Branch, Iran

10.1016/j.joems.2014.06.002

Abstract

In this paper, the notion of mixed f, g monotone mapping is introduced, and the coupled
coincidence point theorem for nonlinear contractive mappings in partially ordered complete metric
spaces has been proved. Presented theorems are generalizations of the recent fixed point theorems
due to Lakshmikantham and C´ iric´ (2009) [17] and include several recent developments. Also, using
the theory of countable extension of t-norm, it has been proved that a common fixed point theorem
given in C´ iric´ (2011) [12] hold for a more general classes of t-norms in fuzzy metric spaces. Their
theorem can be used to investigate a large class of problems and has discussed the existence and
uniqueness of solution for a periodic boundary value problem.

Keywords