NONLINEAR CONDITIONS FOR COINCIDENCE POINT AND FIXED POINT THEOREMS - Du, Wei-Shih; Zheng, Shao-Xuan (Taiwanese journal of mathematics, 2012)
In this paper, we first establish some new types of fixed point theorem which generalize and improve Berinde-Berinde's fixed point theorem, Mizoguchi- Takahashi's fixed point theorem and many results in [W.-S. Du, Some new results and generalizations in metric fixed point theory, Nonlinear Anal. 73 (2010), 1439-1446] and references therein. Applying those new results, we also present some existence theorems of coincidence point and others. 2010Mathematics Subject Classification: 47H10, 54H25. Key words and phrases: Coincidence point,τ-function,τ 0-metric, Function of contractive factor, ℳ𝒯-function, Generalized Berinde-Berinde's fixed point theorem, Generalized Mizoguchi-Takahashi's fixed point theorem.