| Summary: | In this paper, we first propose the concepts of <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>ζ</mi><mo>,</mo><mi>η</mi><mo>,</mo><mi>λ</mi><mo>,</mo><mi>π</mi><mo>)</mo></mrow></semantics></math></inline-formula>-generalized hybrid multi-valued mappings, the set of all the common attractive points (<inline-formula><math display="inline"><semantics><mrow><mi>C</mi><msub><mi>A</mi><mrow><mi>f</mi><mo>,</mo><mi>g</mi></mrow></msub></mrow></semantics></math></inline-formula>) and the set of all the common strongly attractive points (<inline-formula><math display="inline"><semantics><mrow><msub><mi>C</mi><mi>s</mi></msub><msub><mi>A</mi><mrow><mi>f</mi><mo>,</mo><mi>g</mi></mrow></msub></mrow></semantics></math></inline-formula>), respectively for the multi-valued mappings <i>f</i> and <i>g</i> in a CAT(0) space. Moreover, we give some elementary properties in regard to the sets <inline-formula><math display="inline"><semantics><msub><mi>A</mi><mi>f</mi></msub></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><msub><mi>F</mi><mi>f</mi></msub></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><mi>C</mi><msub><mi>A</mi><mrow><mi>f</mi><mo>,</mo><mi>g</mi></mrow></msub></mrow></semantics></math></inline-formula> for the multi-valued mappings <i>f</i> and <i>g</i> in a complete CAT(0) space. Furthermore, we present a weak convergence theorem of common attractive points for two <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>ζ</mi><mo>,</mo><mi>η</mi><mo>,</mo><mi>λ</mi><mo>,</mo><mi>π</mi><mo>)</mo></mrow></semantics></math></inline-formula>-generalized hybrid multi-valued mappings in the above space by virtue of Banach limits technique and Ishikawa iteration respectively. Finally, we prove strong convergence of a new viscosity approximation method for two <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>ζ</mi><mo>,</mo><mi>η</mi><mo>,</mo><mi>λ</mi><mo>,</mo><mi>π</mi><mo>)</mo></mrow></semantics></math></inline-formula>-generalized hybrid multi-valued mappings in CAT(0) spaces, which also solves a kind of variational inequality problem.
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