A GENERALIZED CONTRACTION PRINCIPLE IN MENGER SPACES USING A CONTROL FUNCTION
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 giv...
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| Published in | Analysis in theory & applications Vol. 26; no. 2; pp. 110 - 121 |
|---|---|
| Main Authors | , |
| 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 |
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| Online Access | Get full text |
| ISSN | 1672-4070 1573-8175 |
| DOI | 10.1007/s10496-010-0110-3 |
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| Abstract | 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. |
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| AbstractList | TN1; 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. 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. |
| Author | E N. Dutta Binayak S. Choudhury |
| AuthorAffiliation | Government College of Engineering and Ceramic Technology, India Bengal Engineering and Science University, India |
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| Keywords | ψ ϕ, ψ contraction Menger space fixed point 54H25 (φ,ψ1,ψ2)-contraction |
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| Notes | 32-1631/O1 O189.2 TU857 Menger space, fixed point, （φ, ψ1, ψ2）-contraction |
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| References | Žikić-Došenović (CR31) 2005; 151 Choudhury, Dutta (CR3) 2000; 14 Choudhury, Das (CR6) 2008; 24 Sehgal, Bharucha-Reid (CR28) 1972; 6 Dutta, Choudhury, Das (CR9) 2009; 4 Choudhury (CR4) 2005; 10 Singh, Jain (CR29) 2005; 301 Hadžić, Pap (CR11) 2002; 127 Hadžić, Pap, Budinčević (CR12) 2005; 156 Mihet (CR21) 2009; 71 Choudhury, Dutta (CR5) 2005; 31 Choudhury, Das (CR8) 2009; 42 CR10 Mihet (CR20) 2006; 157 Schweizer, Sklar (CR27) 1983 Suzuki (CR30) 2008; 136 Hicks (CR13) 1983; 13 Sastry, Naidu, Babu, Naidu (CR26) 2000; 31 Mihet (CR18) 2005; 304 Mihet (CR17) 1999; XXXVII Arvanitakis (CR1) 2003; 131 Razani, Shirdaryazdi (CR24) 2007; 32 Liu, Li (CR16) 2007; 158 Mihet (CR19) 2005; 156 Sastry, Babu (CR25) 1999; 30 Choudhury, Das, Dutta (CR7) 2009; 122 Kirk (CR14) 2003; 277 Khan, Swaleh, Sessa (CR15) 1984; 30 Merryfield, Rothschild, Stein (CR22) 2002; 130 Naidu (CR23) 2003; 53 Babu, Lalitha, Sandhya (CR2) 2007; 10 Y. Liu (110_CR16) 2007; 158 S. V. R. Naidu (110_CR23) 2003; 53 B. Schweizer (110_CR27) 1983 G. V. R. Babu (110_CR2) 2007; 10 B. S. Choudhury (110_CR6) 2008; 24 P. N. Dutta (110_CR9) 2009; 4 D. Mihet (110_CR17) 1999; XXXVII K. P. R. Sastry (110_CR26) 2000; 31 W. A. Kirk (110_CR14) 2003; 277 B. S. Choudhury (110_CR3) 2000; 14 T. Žikić-Došenović (110_CR31) 2005; 151 J. Merryfield (110_CR22) 2002; 130 K. P. R. Sastry (110_CR25) 1999; 30 O. Hadžić (110_CR12) 2005; 156 B. S. Choudhury (110_CR7) 2009; 122 D. Mihet (110_CR19) 2005; 156 B. Singh (110_CR29) 2005; 301 B. S. Choudhury (110_CR4) 2005; 10 D. Mihet (110_CR20) 2006; 157 D. Mihet (110_CR18) 2005; 304 B. S. Choudhury (110_CR8) 2009; 42 T. Suzuki (110_CR30) 2008; 136 T. L. Hicks (110_CR13) 1983; 13 D. Mihet (110_CR21) 2009; 71 V.M. Sehgal (110_CR28) 1972; 6 110_CR10 A. Razani (110_CR24) 2007; 32 M. S. Khan (110_CR15) 1984; 30 O. Hadžić (110_CR11) 2002; 127 A. D. Arvanitakis (110_CR1) 2003; 131 B. S. Choudhury (110_CR5) 2005; 31 |
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| Snippet | 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... TN1; 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... |
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| SubjectTerms | 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 |
| Title | A GENERALIZED CONTRACTION PRINCIPLE IN MENGER SPACES USING A CONTROL FUNCTION |
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