Abstract
In this paper, we study minimal and maximal fixed point theorems and iterative technique for nonlinear operators in product spaces. As a corollary of our result, some coupled fixed point theorems are obtained, which generalize the coupled fixed point theorems obtained by Guo Da-jun and Lankshmikantham[2] and the results obtained by Lan in [4], and [6].
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References
Ladde, G. S., V. Lakshmikantham and A. S. Vatsala, Monotone Iterative techniques for nonlinear differential equations. Pitman (1985).
Guo Da-jun and V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications,Nonlinear Anal.,11 (1987), 623–632.
Martin, R. H.,Nonlinear Operators and Differential Equation, Wiley, New York (1976).
Lan Kun-quan, Mixed monotone maps, increasing maps and fixed points,J. Sichuan Normal University (to appear).(in Chinese)
Yu Qing-yu, Fixed point theorems for condensing maps,Acta Mathematics,24 (1981), 430–435. (in Chinese).
Lan Kun-quan, Coupled fixed points for mixed monotone condensing maps,J. Sichuan Normal University (to appear). (in Chinese)
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The project supported by the National Natural Science Foundation of China
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Kun-quan, L., Xie-ping, D. Minimal and maximal fixed point theorems and iterative technique for nonlinear operators in product spaces. Appl Math Mech 13, 227–231 (1992). https://doi.org/10.1007/BF02457368
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DOI: https://doi.org/10.1007/BF02457368