Weak contraction condition involving cubic terms of \(d(x, y)\) under the fixed point consideration (Q355839)
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scientific article; zbMATH DE number 6191222
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Weak contraction condition involving cubic terms of \(d(x, y)\) under the fixed point consideration |
scientific article; zbMATH DE number 6191222 |
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Weak contraction condition involving cubic terms of \(d(x, y)\) under the fixed point consideration (English)
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25 July 2013
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Summary: A fixed point theorem is presented for single-valued map with using generalized \(\varphi\)-weak contractive condition involving various combinations of \(d(x, y)\) on a complete metric space. Our result is an extension as well as a generalization of \textit{Ya. I. Alber} and \textit{S. Guerre-Delabriere} [New results in operator theory and its applications: the Israel M. Glazman memorial volume. Oper. Theory, Adv. Appl. 98, 7--22 (1997; Zbl 0897.47044)] in particular. It also generalizes the results of \textit{B. E. Rhoades} [Nonlinear Anal., Theory Methods Appl. 47, No. 4, 2683--2693 (2001; Zbl 1042.47521)], \textit{B. S. Choudhury} and \textit{P. N. Dutta} [Filomat 14, 43--48 (2000; Zbl 1012.54047)], and \textit{P. N. Dutta} and \textit{B. S. Choudhury} [Fixed Point Theory Appl. 2008, Article ID 406368, 8 p. (2008; Zbl 1177.54024)].
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