## A New Iterative Algorithm for Total Asymptotically Non-Expansive Mapping in CAT(0) Spaces

Samir Dashputre *

Department of Mathematics, Shahid Durwasha Nishad Govt. College, Arjunda, Dist.- Balod (C.G.), 491225, India.

Rakesh Tiwari

Department of Mathematics, Govt. V.Y.T. PG Autonomous College, Durg (C.G.), 491001, India.

Jaynendra Shrivas

Department of Mathematics, Govt. V.Y.T. PG Autonomous College, Durg (C.G.), 491001, India.

*Author to whom correspondence should be addressed.

### Abstract

In this paper, we provide certain fixed point results for a total asymptotically non-expansive mapping, as well as a new iterative algorithm for approximating the fixed point of this class of mappings in the setting of CAT(0) spaces. Furthermore, we establish strong and \(\Delta\)-converges theorem for total asymptotically non-expansive mapping in CAT(0) space. Our result, generalizes, improve, extend and unify the results of Thakur et al. [1], Izhar et al. [2] and many more in this direction.

Keywords: CAT (0) space, total asymptotically non-expansive mappings, strong and \(\Delta\)-convergence theorems.

**How to Cite**

*Asian Research Journal of Mathematics*,

*19*(11), 24–35. https://doi.org/10.9734/arjom/2023/v19i11750

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