A GENERALIZED CONTRACTION PRINCIPLE IN MENGER SPACES USING A CONTROL FUNCTION

• Published in: Analysis in theory & applications Vol. 26; no. 2; pp. 110 - 121
• Main Authors: Dutta, P. N., Choudhury, Binayak S.
• Format: Journal Article
• Language: English
• Published: Heidelberg Editorial Board of Analysis in Theory and Applications 01.06.2010; Department of Mathematics Government College of Engineering and Ceramic Technology 73 A. C. Banerjee Lane, Kolkata-700010, West Bengal India%Department of Mathematics Bengal Engineering and Science University, Shibpur P. O. -B. Garden, Shibpur, Howrah-711103 West Bengal India
• Subjects: Analysis; Approximations and Expansions; Mathematics; Mathematics and Statistics; Menger空间; 不动点定理; 函数; 压缩映射原理; 广义; 控制功能; 概率收缩; ψ; ϕ, ψ; contraction; Menger space; fixed point; 54H25; (φ,ψ1,ψ2)-contraction
• ISSN: 1672-4070; 1573-8175
• DOI: 10.1007/s10496-010-0110-3

In the present paper we use a control function to define a generalized contraction in Menger spaces and obtain a unique fixed point theorem. The work is in line with the research for developing probabilistic contractions with the help of control functions and related fixed point results. We have given an example to which our theorem is applicable. Some corollaries are also discussed.