Some Results for CAT(0) Spaces

الموضوعات :

M. Asadi ¹ (Department of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, Iran.)
S.M. Vaezpour ² (Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran.)
M. Soleymani ³ (Department of Mathematics, Malayer Branch, Islamic Azad University, Malayer, Iran.)

تاريخ الإرسال : 17 الأربعاء , ذو الحجة, 1436 تاريخ التأكيد : 17 الأربعاء , ذو الحجة, 1436 تاريخ الإصدار : 21 الأربعاء , جمادى الثانية, 1434

الکلمات المفتاحية: fixed point, CAT(0) space, Hyperbolic space,

ملخص المقالة :

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

المصادر:

[1] L. Leustean, A quadratic rate of asymptotic regularity for CAT(0)-spaces, J.
Math. Anal. Appl. 325, (2007), 386-399.
[2] S. Dhompongsa and B. Panyanak, On 4-convergence theorems in CAT(0)
spaces, Comput. Math. Appl. 56, (2008), 2572-2579.

[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.