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Nonlinear coupled fixed point theorems in ordered generalized metric spaces with integral type. (English) Zbl 1348.54044

Summary: In this article, we study coupled coincidence and coupled common fixed point theorems in ordered generalized metric spaces for nonlinear contraction condition related to a pair of altering distance functions. Our results generalize and modify several comparable results in the literature.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
54E50 Complete metric spaces
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[1] Ran, ACM; Reurings, MCB, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc Am Math Soc, 132, 1435-1443, (2004) · Zbl 1060.47056
[2] Nieto, JJ; López, RR, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22, 223-239, (2005) · Zbl 1095.47013
[3] Nieto, JJ; López, RR, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math Sinica Engl Ser, 23, 2205-2212, (2007) · Zbl 1140.47045
[4] Agarwal, RP; El-Gebeily, MA, O’regan D: generalized contractions in partially ordered metric spaces, Appl Anal, 87, 1-8, (2008) · Zbl 1140.47042
[5] O’Regan, D; Petrutel, A, Fixed point theorems for generalized contractions in ordered metric spaces, J Math Anal Appl, 341, 241-1252, (2008) · Zbl 1142.47033
[6] Bhaskar, TG; Lakshmikantham, V, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal, 65, 1379-1393, (2006) · Zbl 1106.47047
[7] Lakshmikantham, V; Cirić, LJ, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal, 70, 4341-4349, (2009) · Zbl 1176.54032
[8] Abbas, M; Cho, YJ; Nazir, T, Common fixed point theorems for four mappings in TVS-valued cone metric spaces, J Math Inequal, 5, 287-299, (2011) · Zbl 1220.54017
[9] Abbas, M; Khan, MA; Radenović, S, Common coupled fixed point theorem in cone metric space for \(w\)-compatible mappings, Appl Math Comput, 217, 195-202, (2010) · Zbl 1197.54049
[10] Cho, YJ; He, G; Huang, NJ, The existence results of coupled quasi-solutions for a class of operator equations, Bull Korean Math Soc, 47, 455-465, (2010) · Zbl 1200.47075
[11] Cho, YJ; Saadati, R; Wang, S, Common fixed point theorems on generalized distance in order cone metric spaces, Comput Math Appl, 61, 1254-1260, (2011) · Zbl 1217.54041
[12] Cho, YJ; Shah, MH; Hussain, N, Coupled fixed points of weakly \(F\)-contractive mappings in topological spaces, Appl Math Lett, 24, 1185-1190, (2011) · Zbl 1214.54033
[13] Ciric LJ, Cakic N, Rajovic M, Ume JS: Monotone generalized nonlinear contractions in partially ordered metric spaces.Fixed Point Theory Appl 2008.,2008(11): (ID 131294) · Zbl 1158.54019
[14] Gordji, ME; Cho, YJ; Baghani, H, Coupled fixed point theorems for contractions in intuitionistic fuzzy normed spaces, Math Comput Model, 54, 1897-1906, (2011) · Zbl 1235.47094
[15] Graily, E; Vaezpour, SM; Saadati, R; Cho, YJ, Generalization of fixed point theorems in ordered metric spaces concerning generalized distance, Fixed Point Theory Appl, 2011, 30, (2011) · Zbl 1270.54041
[16] Karapinar, E, Couple fixed point theorems for nonlinear contractions in cone metric spaces, (2010) · Zbl 1198.65097
[17] Sabetghadam, F; Masiha, HP; Sanatpour, AH, Some coupled fixed point theorems in cone metric spaces, Fixed point Theory Appl, 2009, 8, (2009) · Zbl 1179.54069
[18] Samet, B, Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal, 72, 4508-4517, (2010) · Zbl 1264.54068
[19] Samet, B; Vetro, C, Coupled fixed point, \(F\)-invariant set and fixed point of \(N\)-order, Ann Funct Anal, 1, 46-56, (2010) · Zbl 1214.54041
[20] Samet, B; Yazidi, H, Coupled fixed point theorems in partially ordered \(ε\)-chainable metric spaces, J Math Comput Sci, 1, 142-151, (2010)
[21] Sintunavarat, W; Cho, YJ; Kumam, P, Common fixed point theorems for \(c\)-distance in ordered cone metric spaces, Comput Math Appl, 62, 1969-1978, (2011) · Zbl 1231.54028
[22] Sintunavarat, W; Cho, YJ; Kumam, P, Coupled coincidence point theorems for contractions without commutative condition in intuitionistic fuzzy normed spaces, Fixed Point Theory Appl, 2011, 81, (2011) · Zbl 1315.47049
[23] Zhu, XH; Xiao, JZ, Note on “Coupled fixed point theorems for contractions in fuzzy metric spaces”, Nonlinear Anal, 72, 5475-5479, (2011) · Zbl 1220.54040
[24] Shatanawi, W, Partially ordered cone metric spaces and coupled fixed point results, Comput Math Appl, 60, 2508-2515, (2010) · Zbl 1205.54044
[25] Mustafa, Z; Sims, B, A new approach to generalized metric spaces, J Nonlinear Convex Anal, 7, 289-297, (2006) · Zbl 1111.54025
[26] Abbas, M; Rhoades, BE, Common fixed point results for non-commuting mappings without continuity in generalized metric spaces, Appl Math Comput, 215, 262-269, (2009) · Zbl 1185.54037
[27] Chugh, R; Kadian, T; Rani, A; Rhoades, BE, Property \(p\) in \(G\)-metric spaces, Fixed Point Theory Appl, 2010, 12, (2010) · Zbl 1203.54037
[28] Mustafa, Z; Sims, B, Some remarks concerning \(D\)-metric spaces, 189-198, (2003), Spain · Zbl 1079.54017
[29] Mustafa, Z; Obiedat, H; Awawdehand, F, Some fixed point theorem for mapping on complete \(G\)-metric spaces, Fixed Point Theory Appl, 2008, 12, (2008) · Zbl 1148.54336
[30] Mustafa, Z; Sims, B, Fixed point theorems for contractive mapping in complete G- metric spaces, Fixed Point Theory Appl, 2009, 10, (2009) · Zbl 1179.54067
[31] Mustafa, Z; Shatanawi, W; Bataineh, M, Existence of fixed point results in \(G\)-metric spaces, Int J Math Anal, 2009, 10, (2009) · Zbl 1179.54066
[32] Shatanawi, W, Fixed point theory for contractive mappings satisfying φ-maps in \(G\)-metric spaces, Fixed Point Theory Appl, 2010, 9, (2010) · Zbl 1204.54039
[33] Abbas, M; Khan, AR; Nazir, T, Coupled common fixed point results in two generalized metric spaces, (2011) · Zbl 1210.54048
[34] Shatanawi, W, Coupled fixed point theorems in generalized metric spaces, Hacet J Math Stat, 40, 441-447, (2011) · Zbl 1230.54047
[35] Saadati, R; Vaezpour, SM; Vetro, P; Rhoades, BE, Fixed point theorems in generalized partially ordered \(G\)-metric spaces, Math Comput Model, 52, 797-801, (2010) · Zbl 1202.54042
[36] Choudhury, BS; Maity, P, Coupled fixed point results in generalized metric spaces, Math Comput Model, 54, 73-79, (2011) · Zbl 1225.54016
[37] Khan, MS; Swaleh, M; Sessa, S, Fixed point theorems by altering distancces between the points, Bull Aust Math Soc, 30, 1-9, (1984) · Zbl 0553.54023
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