^{1}Department of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, Iran.

^{2}Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran.

^{3}Department of Mathematics, Malayer Branch, Islamic Azad University, Malayer, Iran.

Abstract

We shall generalize the concept of z = (1-t)+ty to n times which contains to verify some their properties and inequalities in CAT(0) spaces. In the sequel with introducing of -nonexpansive mappings, we obtain some xed points and approximate fixed points theorems.

Article Title [Persian]

Some Results for CAT(0) Spaces

Authors [Persian]

M. Asadi^{1}; S.M. Vaezpour^{2}; M. Soleymani^{3}

^{1}Department of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, Iran.

^{2}Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran,
Iran.

^{3}Department of Mathematics, Malayer Branch, Islamic Azad University, Malayer, Iran.

Abstract [Persian]

We shall generalize the concept of z = (1-t)+ty to n times which contains to verify some their properties and inequalities in CAT(0) spaces. In the sequel with introducing of -nonexpansive mappings, we obtain some xed points and approximate fixed points theorems.

Keywords [Persian]

CAT(0) space، Hyperbolic space، fixed point

References

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[3] F. Bruhat and J. Tits, Groupes reductifs sur un corps local. I. Donnees radicielles valuees, Inst. Hautes Etudes Sci. Publ. Math. 41, (1972), 5-251. [4] M. Bridson and A. Hae iger, Metric Spaces of Non-Positive Curvature, Springer- Verlag, Berlin, Heidelberg, 1999. [5] T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings,J. Math. Anal. Appl. 340, (2008), 1088-1095. [6] B. Nanjaras and B. Panyanaka and W. Phuengrattana, Fixed point theorems and convergence theorems for Suzuki-generalized nonexpansive mappings in CAT(0) spaces, Nonlinear Anal.: Hybrid Systems, 4, (2010), 25-31. [7] A. Razani and H. Salahifard, Invariant approximation for CAT(0) spaces, Non- linear Anal. (TMA), 72, (2010), 2421-2425. [8] P. Chaoha and A. Phon-on, A note on xed point sets in CAT(0) spaces, J. Math. Anal. Appl. 320, (2006), 983-987. [9] K. Goebel and W. A. Kirk, Some problems in metric xed point theory, J. of Fixed Point Theory and Appl. 4, (2008), 13-25. [10] M. Asadi, S. M. Vaezpour and H. Soleimani, -Nonexpansive Mappings on CAT(0) Spaces, World Appl. Sci. J. 11, (2010), 1303-1306.