在本文中，我們要先介紹一個錐球度量空間的概念，並推得在錐球度量空間中，滿足收縮型的強Meir-Keeler錐型函數有固定點。

In this paper, we introduce the concept of cone ball-metric spaces and we prove fixed point results on such spaces for mappings satisfying a contraction involving a stronger Meir-Keeler cone-type function.

[1] M. Abbas, G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone uniform spaces, J Math. Anal. Appl.,341(2008)No.1,416-420.
[2] C. Di Bari, P. Vetro, -paris and common fixed points in cone metric spaces, Rendiconti del Cirolo Mathematico di Palermo,57(2008)279-285.DOI:10.1007/512215-008-0020-9.
[3] C. Di Bari, T. Suzuki, P. Vetro, Best proximity for cyclic Meir-Keeler contractions, Nonlinear Anal.,69 (2008) 3790-3794.
[4] Binayak S. Choudhury and N. Metiya, Fixed points of weak contractions in cone metric spaces, Nonlinear Analysis, Nonlinear Anal.,72(2010)1589-1593.
[5] W. Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Anal.,72(2010),2259-2261.
[6] L. G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl.322(2007), 1468-1476.
[7] D. Ilic′, S. Radenovic′, Common fixed points for maps on cone metric spaces, J. Math. Anal. Appl.,341(2008)No.2,876-882.
[8] S. Jankovic′, Z. Kadelburg, S . Radonevic, B. E. Rhoades, Assad-Kirk-type fixed point theorems for a pair of nonself mappings on cone metric spaces, Fixed Point Theory and Applications,2009 Vol. 2009,16 pages, Article ID 761086,doi:10.1155/2009/761086.
[9] S. Jankovic, Z. Kadelburg, S. Radonevic, B. E. Rhoades, Best proximity point Theorems for p-cyclic Meir-Keeler contractions, Fixed Point Theory and Applications,2009 Vol. 2009, 9 pages, Article ID 197308, doi:10.1155/2009/197308.
[10] A. Meir and E, Keeler, A theorem on contraction mappings, J. Math.Anal.Appl.,28(1969), 326-329.
[11] N. Mizoguchi and W. Takahashi, Fixed point theorems for multivalued mappingson complete metric spaces, J. Math. Anal. Appl.,141(1989) 177-188.
[12] Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J.Nonlinear and Convex. Anal.,7(2006) No.2, 289-297.
[13] Sh. Rezapour, R. Hamlbarani, Some notes on the paper “Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl.,345(2008)719-724.
[14] B. Samet, Ćirićs fixed point theorem in a cone metric space, J. Nonlinear Sci. Appl.,3(4)
(2010)302-308.
[15] A. Sonmez, On paracompactness in cone metric spaces, Allpied Mathematics Letters.,23
(2010)494-497.
[16] W. Shatanawi, Fixed point theory for contractive mappings satisfying -maps in G-metric spaces, Fixed point theory and applications, Vol.2010 Article ID 181650,9pages doi:10.1155/2010/181650.
[17] T. Suzuki, Fixed-point theorem for asymptotic contractions of Meir-Keeler type in complete metric spaces, Nonlinear Anal.,6464 (2006), 971-978.
[18] T. Suzuki, Moudafis viscosity approximations with Meir-Keeler contractions, J. Math. Anal. Appl.,325(2007), 342-352.
[19] D. Wardowski, On set-valued contractions of Nadler type in cone metric spaces, Applied Mathematics Letters.,24(3)(2011),275-278.
[20] P.P. Zabrejko, K-metric and K-normed linear spaces: survey, Collect. Math.,48.4-6(1997),
825-859.