Coupled fixed points of contraction maps with a rational expression in partially ordered metric spaces
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The purpose of this paper is to extend the fixed point results of maps satisfying weak contractivity condition introduced by Bhaskar and Lakshmikantam [T. Gnana Bhaskar and V. Lakshmikantham, Fixed point theorem in partially ordered metric spaces and applications, Non-linear Analysis, 65 (2006), 1379-1393] to the case of contractions with rational expressions in partially ordered metric spaces. Examples are provided in support of our results. Our theorems generalize the results of Bhaskar and Lakshmikantam [2].
Abstract
The purpose of this paper is to extend the fixed point results of maps satisfying weak contractivity condition introduced by Bhaskar and Lakshmikantam [T. Gnana Bhaskar and V. Lakshmikantham, Fixed point theorem in partially ordered metric spaces and applications, Non-linear Analysis, 65 (2006), 1379-1393] to the case of contractions with rational expressions in partially ordered metric spaces. Examples are provided in support of our results. Our theorems generalize the results of Bhaskar and Lakshmikantam [2].
참고문헌 (10)
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- D.S. Jaggi, "Some unique fixed point theorems", Indian Journal of Pure and Applied Mathematics, 8, pp.223~230 (1977)
- V. Lakshmikantham, "Coupled fixed point theorems for non liner contractions in partially ordered metric spaces", Non-linear Analysis, 70, pp.4341~4349 (2009)
- Nguyen Van Luong, "Coupled fixed point theorems in partially ordered metric spaces", Bulletin of Mathematical Analysis and Applications, 2(4), pp.16~24 (2010)
- Nguyen Van Luong, "Coupled fixed point theorems in partially ordered metric space depended on another function", Bulletin of Mathematical Analysis and Applications, 3(3), pp.129~140 (2011)
- B. Samet, "The coupled fixed point theorems in partially ordered ϵ-chainable metric spaces", The Journal of Mathematics and Computer Science, 1(3), pp.142~151 (2010)