Brijesh Kumar Tripathi - Department of Mathematics, L. D. College of Engineering, Ahmedabad, Gujarat-۳۸۰۰۱۵, India.
V. K. Chaubey - Department of Applied Sciences, Buddha Institute of Technology, GIDA Gorakhpur, U.P., ۲۷۳۲۰۹, INDIA

The purpose of present paper to determine the Finsler spaces due to deformation of special Finsler (\alpha, \beta) -metric. Consequently, we obtained the non-holonomic frame with the help of \alpha^{۲}=a_{ij}(x)y^{i}y^{j} , one form metric \beta=b_{i}(x)y^{i} and infinite series of (\alpha, \beta) metric such as the forms I.\;\; (\frac{\beta^{۴}}{(\beta-\alpha)^{۲}})+\alpha^{۲} =F_{۱}^{۲}+F_{۲}^{۲} i.e. sum of the square of infinite series of (\alpha, \beta) -metric and square of Riemannian metric II.\;\;(\frac{\beta^{۴}}{(\beta-\alpha)^{۲}})+\beta^{۲} =F_{۱}^{۲}+F_{۳}^{۲} i.e. sum of the square of infinite series of (\alpha, \beta) -metric and square of ۱-form metric.

Riemannian metric, One form metric, Infinite series of (\alpha, \beta) -metric, Nonholonomic Finsler frame