Linking contractive self-mappings and cyclic Meir-Keeler contractions with Kannan self-mappings. (English) Zbl 1194.54059

Summary: Some mutual relations between \(p\)-cyclic contractive self-mappings, \(p\)-cyclic Kannan self-mappings, and Meir-Keeler \(p\)-cyclic contractions are stated. On the other hand, related results about the existence of the best proximity points and existence and uniqueness of fixed points are also formulated.


54H25 Fixed-point and coincidence theorems (topological aspects)
Full Text: DOI EuDML


[1] Dominguez Benavides, T; Phothi, S, The fixed point property under renorming in some classes of Banach spaces, Nonlinear Analysis: Theory, Methods &Applications, 72, 1409-1416, (2010) · Zbl 1194.46021
[2] Suzuki, T, A new type of fixed point theorem in metric spaces, Nonlinear Analysis: Theory, Methods & Applications, 71, 5313-5317, (2009) · Zbl 1179.54071
[3] Burgić, Dž; Kalabušić, S; Kulenović, MRS, Global attractivity results for mixed-monotone mappings in partially ordered complete metric spaces, No. 2009, 17, (2009) · Zbl 1168.54327
[4] Nieto, JJ; Pouso, RL; Rodríguez-López, R, Fixed point theorems in ordered abstract spaces, Proceedings of the American Mathematical Society, 135, 2505-2517, (2007) · Zbl 1126.47045
[5] Olatinwo, MO, Some common fixed point theorems for selfmappings satisfying two contractive conditions of integral type in a uniform space, Central European Journal of Mathematics, 6, 335-341, (2008) · Zbl 1161.54023
[6] Azhmyakov, V, Convexity of the set of fixed points generated by some control systems, No. 2009, 14, (2009) · Zbl 1175.93102
[7] De la Sen, M, Total stability properties based on fixed point theory for a class of hybrid dynamic systems, No. 2009, 19, (2009) · Zbl 1189.34023
[8] De la Sen, M, About robust stability of dynamic systems with time delays through fixed point theory, No. 2008, 20, (2008) · Zbl 1181.47079
[9] De la Sen, M, Quadratic stability and stabilization of switched dynamic systems with uncommensurate internal point delays, Applied Mathematics and Computation, 185, 508-526, (2007) · Zbl 1108.93062
[10] De la Sen, M, On the robust adaptive stabilization of a class of nominally first-order hybrid systems, IEEE Transactions on Automatic Control, 44, 597-602, (1999) · Zbl 1056.93616
[11] Meir, A; Keeler, E, A theorem on contraction mappings, Journal of Mathematical Analysis and Applications, 28, 326-329, (1969) · Zbl 0194.44904
[12] Karpagam, S; Agrawal, S, Best proximity point theorems for [inlineequation not available: see fulltext.]-cyclic Meir-Keeler contractions, No. 2009, 9, (2009) · Zbl 1172.54028
[13] Chen, C-M; Chang, T-H, Fixed point theorems for a weaker Meir-Keeler type [inlineequation not available: see fulltext.]-set contraction in metric spaces, No. 2009, 8, (2009)
[14] Eldred, AA; Veeramani, P, Existence and convergence of best proximity points, Journal of Mathematical Analysis and Applications, 323, 1001-1006, (2006) · Zbl 1105.54021
[15] Kikkawa, M; Suzuki, T, Some similarity between contractions and Kannan mappings, No. 2008, 8, (2008) · Zbl 1162.54019
[16] Enjouji, Y; Nakanishi, M; Suzuki, T, A generalization of Kannan’s fixed point theorem, No. 2009, 10, (2009) · Zbl 1179.54056
[17] De la Sen, M, Some combined relations between contractive mappings, Kannan mappings, reasonable expansive mappings, and [inlineequation not available: see fulltext.]-stability, No. 2009, 25, (2009) · Zbl 1179.54054
[18] Inoue, G; Takahashi, W; Zembayashi, K, Strong convergence theorems by hybrid methods for maximal monotone operators and relatively nonexpansive mappings in Banach spaces, Journal of Convex Analysis, 16, 791-806, (2009) · Zbl 1194.47083
[19] Aoyama, K; Kohsaka, F; Takahashi, W, Strongly relatively nonexpansive sequences in Banach spaces and applications, Journal of Fixed Point Theory and Applications, 5, 201-225, (2009) · Zbl 1269.47037
[20] Chen, C; Zhu, C, Fixed point theorems for [inlineequation not available: see fulltext.] times reasonable expansive mapping, No. 2008, 6, (2008)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.