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Fixed point theorems for mixed monotone operators and applications to integral equations. (English) Zbl 1218.54040
The authors generalize Theorem 1 of [T. G. Bhaskar and V. Lakshmikantham, Nonlinear Anal., Theory Methods Appl. 65, No. 7, A, 1379–1393 (2006; Zbl 1106.47047)] by using altering distance functions and present some coupled fixed point theorems for a mixed monotone operator in a complete metric space endowed with a partial order. They also provide an application to integral equations.

MSC:
54H25Fixed-point and coincidence theorems in topological spaces
54E50Complete metric spaces
54F05Linearly, generalized, and partial ordered topological spaces
References:
[1]Guo, D.; Lakshmikantham, V.: Coupled fixed points of nonlinear operators with applications, Nonlinear anal. 11, 623-632 (1987) · Zbl 0635.47045 · doi:10.1016/0362-546X(87)90077-0
[2]Guo, D.; Lakshmikantham, V.: Nonlinear problems in abstract cones, (1988)
[3]Guo, D.: Existence and uniqueness of positive fixed point for mixed monotone operators with applications, Appl. anal. 46, 91-100 (1992) · Zbl 0792.47053 · doi:10.1080/00036819208840113
[4]Zhang, Z.: New fixed point theorems of mixed monotone operators and applications, J. math. Anal. appl. 204, 307-319 (1996) · Zbl 0880.47036 · doi:10.1006/jmaa.1996.0439
[5]Zhang, S. S.; Ma, Y. H.: Coupled fixed points for mixed monotone condensing operators and an existence theorem of the solution for a class of functional equations arising in dynamic programming, J. math. Anal. appl. 160, 468-479 (1991) · Zbl 0753.47029 · doi:10.1016/0022-247X(91)90319-U
[6]Sun, Y.: A fixed point theorem for mixed monotone operator with applications, J. math. Anal. appl. 156, 240-252 (1991) · Zbl 0761.47040 · doi:10.1016/0022-247X(91)90394-F
[7]Bhaskar, T. G.; Lakshmikantham, V.: Fixed point theorems in partially ordered metric spaces and applications, Nonlinear anal. 65, 1379-1393 (2006) · Zbl 1106.47047 · doi:10.1016/j.na.2005.10.017
[8]Agarwal, R. P.; El-Gebeily, M. A.; O’regan, D.: Generalized contractions in partially ordered metric spaces, Appl. anal. 87, 109-116 (2008) · Zbl 1140.47042 · doi:10.1080/00036810701556151
[9]Burgic, Dz.; Kalabusic, S.; Kulenovic, M. R. S.: Global attractivity results for mixed monotone mappings in partially ordered complete metric spaces, Fixed point theory appl. (2009) · Zbl 1168.54327 · doi:10.1155/2009/762478
[10]Ciric, L.; Cakid, N.; Rajovic, M.; Ume, J. S.: Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed point theory appl. (2008) · Zbl 1158.54019 · doi:10.1155/2008/131294
[11]Harjani, J.; Sadarangani, K.: Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear anal. 71, 3403-3410 (2009) · Zbl 1221.54058 · doi:10.1016/j.na.2009.01.240
[12]Harjani, J.; Sadarangani, K.: Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear anal. 72, 1188-1197 (2010) · Zbl 1220.54025 · doi:10.1016/j.na.2009.08.003
[13]Harjani, J.; Sadarangani, K.: Fixed point theorems for mappings satisfying a condition of integral type in partially ordered sets, J. convex anal. 17, 597-609 (2010) · Zbl 1192.54018 · doi:http://www.heldermann.de/JCA/JCA17/JCA172/jca17040.htm
[14]Lakshmikantham, V.; Ciric, L.: Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear anal. 70, 4341-4349 (2009) · Zbl 1176.54032 · doi:10.1016/j.na.2008.09.020
[15]Nieto, J. J.; Rodríguez-López, R.: Existence of extremal solutions for quadratic fuzzy equations, Fixed point theory appl., 321-342 (2005) · Zbl 1102.54004 · doi:10.1155/FPTA.2005.321
[16]Nieto, J. J.; Rodríguez-López, R.: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22, 223-239 (2005) · Zbl 1095.47013 · doi:10.1007/s11083-005-9018-5
[17]Nieto, J. J.; Rodríguez-López, R.: Applications of contractive-like mapping principles to fuzzy equations, Rev. math. Comput. 19, 361-383 (2006) · Zbl 1113.26030
[18]Nieto, J. J.; Pouso, R. L.; Rodríguez-López, R.: Fixed point theorems in ordered abstract spaces, Proc. amer. Math. soc. 135, 2505-2517 (2007) · Zbl 1126.47045 · doi:10.1090/S0002-9939-07-08729-1
[19]Nieto, J. J.; Rodríguez-López, R.: Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta math. Sinica 23, 2205-2212 (2007) · Zbl 1140.47045 · doi:10.1007/s10114-005-0769-0
[20]O’regan, D.; Petrusel, A.: Fixed point theorems for generalized contractions in ordered metric spaces, J. math. Anal. appl. 341, 1241-1252 (2008) · Zbl 1142.47033 · doi:10.1016/j.jmaa.2007.11.026
[21]Petrusel, A.; Rus, I. A.: Fixed point theorems in ordered L-spaces, Proc. amer. Math. soc. 134, 411-418 (2006) · Zbl 1086.47026 · doi:10.1090/S0002-9939-05-07982-7
[22]Ran, A. C. M.; Reurings, M. C. B.: A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. amer. Math. soc. 132, 1435-1443 (2004) · Zbl 1060.47056 · doi:10.1090/S0002-9939-03-07220-4
[23]Wu, Y.: New fixed point theorems and applications of mixed monotone operator, J. math. Anal. appl. 341 (2008) · Zbl 1137.47044 · doi:10.1016/j.jmaa.2007.10.063
[24]Cabada, A.; Nieto, J. J.: Fixed points and approximate solutions for nonlinear operator equations, J. comput. Appl. math. 113, 17-25 (2000) · Zbl 0954.47038 · doi:10.1016/S0377-0427(99)00240-X
[25]Khan, M. S.; Swaleh, M.; Sessa, S.: Fixed point theorems by altering distances between the points, Bull. austral. Math. soc. 30, No. 1, 1-9 (1984) · Zbl 0553.54023 · doi:10.1017/S0004972700001659