Coupled coincidence point theorems for mixed monotone nonlinear operators

AbstractWe obtain coupled coincidence and coupled common fixed point theorems for mixed g-monotone nonlinear operators F:X×X→X in partially ordered metric spaces. Our results are generalizations of recent coincidence point theorems due to Lakshmikantham and Ćirić [V. Lakshmikantham, L. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70 (2009) 4341–4349], of coupled fixed point theorems established by Bhaskar and Lakshmikantham [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (7) (2006) 1379–1393] and also include as particular cases several related results in very recent literature

Fixed points and coupled fixed points in partially ordered ν-generalized metric spaces

[EN] New fixed point and coupled fixed point theorems in partially ordered ν-generalized metric spaces are presented. Since the product of two ν-generalized metric spaces is not in general a ν-generalized metric space, a different approach is needed than in the case of standard metric spaces.Abtahi, M.; Kadelburg, Z.; Radenovic, S. (2018). Fixed points and coupled fixed points in partially ordered ν-generalized metric spaces. Applied General Topology. 19(2):189-201. doi:10.4995/agt.2018.7409SWORD189201192M. Abtahi, Fixed point theorems for Meir-Keeler type contractions in metric spaces, Fixed Point Theory 17, no. 2 (2016), 225-236.M. Abtahi, Z. Kadelburg and S. Radenovic, Fixed points of Ciric-Matkowski-type contractions in $nu$-generalized metric spaces, Rev. Real Acad. Cienc. Exac. Fis. Nat. Ser. A, Mat. 111, no. 1 (2017), 57-64.B. Alamri, T. Suzuki and L. A. Khan, Caristi's fixed point theorem and Subrahmanyam's fixed point theorem in $nu$-generalized metric spaces, J. Function Spaces, 2015, Art. ID 709391, 6 pp.V. Berinde and M. Pacurar, Coupled fixed point theorems for generalized symmetric Meir-Keeler contractions in ordered metric spaces, Fixed Point Theory Appl. (2012) 2012:115. https://doi.org/10.1186/1687-1812-2012-115T. G. Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65, no. 7 (2006), 1379-1393. https://doi.org/10.1016/j.na.2005.10.017A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen 57 (2000), 31-37.Lj. B. Ciric, A new fixed-point theorem for contractive mappings, Publ. Inst. Math. (N.S) 30 (44) (1981), 25-27.Z. Kadelburg and S. Radenovic, On generalized metric spaces: A survey, TWMS J. Pure Appl. Math. 5 (2014), 3-13.Z. Kadelburg and S. Radenovic, Fixed point results in generalized metric spaces without Hausdorff property, Math. Sciences 8:125 (2014). https://doi.org/10.1007/s40096-014-0125-6R. Kannan, Some results on fixed points-II, Amer. Math. Monthly 76 (1969), 405-408.W. A. Kirk and N. Shahzad, Generalized metrics and Caristi's theorem, Fixed Point Theory Appl. 2013:129 (2013). https://doi.org/10.1186/1687-1812-2013-129V. Lakshmikantham and Lj. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70 (2009), 4341-4349. https://doi.org/10.1016/j.na.2008.09.020N. V. Luong and N. X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74 (2011), 983-992. https://doi.org/10.1016/j.na.2010.09.055J. J. Nieto and R. Rodríguez-López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sinica, Engl. Ser. 23, no. 12 (2007), 2205-2212. https://doi.org/10.1007/s10114-005-0769-0P. D. Proinov, Fixed point theorems in metric spaces, Nonlinear Anal. 64 (2006), 546-557. https://doi.org/10.1016/j.na.2005.04.044B. Samet, Discussion on 'A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces' by A. Branciari, Publ. Math. Debrecen 76 (2010), 493-494.B. Samet, Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal. 72 (2010), 4508-4517. https://doi.org/10.1016/j.na.2010.02.026I. R. Sarma, J. M. Rao and S. S. Rao, Contractions over generalized metric spaces, J. Nonlinear Sci. Appl. 2 (2009), 180-182. https://doi.org/10.22436/jnsa.002.03.06T. Suzuki, Generalized metric spaces do not have the compatible topology, Abstr. Appl. Anal., 2014, Art. ID 458098, 5 pp.T. Suzuki, B. Alamri and L. A. Khan, Some notes on fixed point theorems in v-generalized metric spaces, Bull. Kyushu Inst. Tech. Pure Appl. Math. 62 (2015), 15-23.M. Turinici, Functional contractions in local Branciari metric spaces, Romai J. 8 (2012),189-199

FIXED POINT THEOREMS FOR A GENERALIZED ALMOST CONTRACTIVE MAPPINGS IN ORDERED METRIC SPACES FOR INTEGRAL TYPE

In this paper, the existence theorems of fixed points and common fixed points for two weakly increasing mappings satisfying a new condition in ordered  metric spaces are proved. Our results extend, generalize and unify most of the fundamental metrical fixed point thaorems in the literature in Integral type mappings. AMS: 47H10, 54H25. Keywords: common fixed point, almost contraction, ordered metric spaces