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

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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 strong convergence to a common element of fixed points 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.

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