Fixed Point Methods and Optimization

Electronic ISSN: 3008-1548

DOI: 10.69829/fpmo

Approximate solutions of nonlinear equations involving some classes of operators in CAT(0) space

Fixed Point Methods and Optimization, Volume 2, Issue 1, April 2025, Pages 21–37

EKENE C. NWANKWOR

Department of Mathematics, Nnamdi Azikiwe University, Awka, Anambra State, Nigeria

OBIAGERI M. EZUGORIE

Department of Mathematics, University of Nigeria, Nsukka, Nigeria

STANLEY C. OKOYEH

Department of Mathematics, Nnamdi Azikiwe University, Awka, Anambra State, Nigeria

NNAMDI N. ARAKA

Department of Mathematics, Federal University of Technology, Owerri, Imo State, Nigeria

GODWIN C. UGWUNNADI

Department of Mathematics, University of Eswatini, Private Bag 4, Kwaluseni, Eswatini

Department of Mathematics and Applied Mathematics, Sefako Makgato Health Science University, P.O. Box 94, Pretoria 0204, South Africa

DERIC U. OFOEDU

Department of Mathematics, Nnamdi Azikiwe University, Awka, Anambra State, Nigeria


Abstract

It is the purpose of this paper to establish \(\triangle\)-demiclosedness principle for uniformly continuous generalized asymptotically \(\eta\)-strictly pseudocontractive operators in CAT(0) spaces. In addition, a modified Halpern-type iterative algorithm is constructed and its convergence to a common element of fixed point set of uniformly continuous asymptotically \(\eta\)-strictly pseudo-contractive operator and set of common solutions of finite collection of monotone inclusion problems is proved in complete CAT(0) space. As application of the results obtained, approximate common solution of finite collection of convex minimization and fixed point problems for uniformly continuous asymptotically \(\eta\)-strictly pseudo-contractive operator is obtained. The theorems proved extend, generalize, improve and unify several existing results in this direction of research.


Cite this Article as

Ekene C. Nwankwor, Obiageri M. Ezugorie, Stanley C. Okoyeh, Nnamdi N. Araka, Godwin C. Ugwunnadi, and Eric U. Ofoedu, Approximate solutions of nonlinear equations involving some classes of operators in CAT(0) space, Fixed Point Methods and Optimization, 2(1), 21–37, 2025