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In the present paper we established some interesting results on purely Hermitian R-complex Finsler space with (α, β)-metrics, Firstly we characterize the conditions for the (α, β)-metric F = p α2 + εβ2 to be a purely Hermitian. Then determined the fundamental metric tensor, its inverse and determinent of the above metric. Further obtained Chern-Finsler connection coefficients and analysed necessary conditions under which an purely Hermitian R-complex Finsler space with (α, β)-metric to be Berwald, Kahler and strongly Kahler also given some examples.

On Purely Hermitian R-complex Finsler Space with (α, β)-Metric