NONLINEAR CONDITIONS FOR COINCIDENCE POINT AND FIXED POINT THEOREMS

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...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 16; no. 3; pp. 857 - 868
Main Authors Du, Wei-Shih, Zheng, Shao-Xuan
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.06.2012
Subjects
Coincidence
Decreasing sequences
Diagonal lemma
Existence theorems
Mathematical functions
Mathematical theorems
Topological theorems
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Summary: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.
ISSN:1027-5487
2224-6851
DOI:10.11650/twjm/1500406661