Deformed Infinite series metric in Cartan Spaces

Igarashi introduce the concept of $(α, β)$-metric in Cartan space $\ell^{n}$ analogously to one in Finsler space and obtained the basic important geometric properties and also investigate the special class of the space with $(α, β)$-metric in $\ell^{n}$ in terms of $'invariants'$. In the present paper we determine the $'invariants'$ in two different cases of deformed infinite series metric which characterize the special classes of Cartan spaces $\ell^{n}$.

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