New Common Fixed Points for Total Asymptotically Nonexpansive Mapping in CAT(0) Space

Main Article Content

Ahmed Jameel Kadhim


      Strong and ∆-convergence for a two-step iteration process utilizing asymptotically nonexpansive and total asymptotically nonexpansive noneslf mappings in the CAT(0) spaces have been studied. As well, several strong convergence theorems under semi-compact and condition (M) have been proved. Our results improve and extend numerous familiar results from the existing literature.


Download data is not yet available.

Article Details

How to Cite
Kadhim AJ. New Common Fixed Points for Total Asymptotically Nonexpansive Mapping in CAT(0) Space. Baghdad Sci.J [Internet]. 2021Dec.1 [cited 2021Dec.4];18(4):1286. Available from:


Abbas M, Ibrahim Y, Khan AR, Sen M. Split variational inclusion problem and fixed point problem for a class of multivalued mappings in CAT(0) spaces. Mathematics. 2019;7(749).

Dhompongsa S, Panyanak B. On ∆-convergence theorems in CAT(0) spaces, Comput. Math. Appl. 2008; 56: 2572-2579.

Khan SH, Abbas M. Strong and ∆-convergence of some iteration schemes in CAT(0) spaces. Comput. Math. Appl. 2011; 61: 109-116.

Saluja GS. On the convergence of modified S-iteration process for generalized asymptotically quasi-nonexpansive mappings CAT(0) spaces. published by faculty of Sci. Math. 2014; 6(2): 29-38.

Saluja GS, Postolache M. Strong and ∆-convergence theorems for two asymptotically nonexpansive mappings in the itermediate sense in CAT(0) spaces. Fixed Point Theory Appl. 2015; 12.

Abkar A, Shekarbaigi M. A novel iteration algorithm applied tp totally asymptotically nonexpansive mappings in CAT(0) spaces. Math. 2017; 5(14).

Kimura Y. Convergence of a sequence of sets in a Hadamard space and the shrinking projection method for a real hilbert ball, Hindawi. Abstract and Applied Analysis, 2010.

Ullah K, Iqbal K, Ashed M. Some convergence results using K iteration process in CAT(0) spaces. Fixed Point Theory Appl. 2018; 11.

Yodav MR. Common fixed point for contractive operators by a faster iteration process in real Banach spaces. J. Comp. Math. Sci. 2014; 5(2): 251-257.

Abed SS, Hasan ZMM. Common fixed point of a finite-step iteration algorithm under total asymptotically quasi-nonexpansive maps. Baghdad Sci. J. 2019; 16(3).

Chang S, Wang L, Jlee HW, Chan C. Strong and ∆-convergence for mixed type total asymptotically nonexpansive mappings in CAT(0) spaces. Fixed Point Theory Appl. 2013; 122.

Abed SS, Hasan ZMM. Multi-step iteration algorithm via two finite families of total asymptotically quasi-nonexpansive maps. ASTESJ. 2019; 4(2).

Uddin I, Dala S, Imdad M. Approximating fixed points for generalized nonexpansive mapping in CAT(0) spaces. J. Inequalities Appl. 2014; 155.

Kazeem OA, Chinedu IZ, Godwin CU, Oluwatosin TM. On the proximal point algorithm and demimetric mappings in CAT(0) spaces. Demonstr. Math. 2018; 51: 277-294.

Godwin CU. Approximating a common fixed point for finite family of demimetric mappings in CAT(0) space. Fixed point theory, 2019; 9(1): 45-60.

Husain S, Singh N. ∆-convergence for proximal point algorithm and fixed point problem in CAT(0) spaces. Fixed Point Theory Appl. 2019; 8.