In this paper, we would like to state well-known Ostrowski inequality via ϕ-λ-convex in 1^st kind by using the SVN-Reimann integrals. In addition, we establish some SVN-Ostrowski type inequalities for the class of functions whose derivatives in absolute values at certain powers are ϕ-λ-convex in 1^st kind by using different techniques including Hölder’s inequality and power mean inequality. We are introducing very first time that the class of ϕ-λ-convex in 1^st kind, which is the generalization of many important classes including class of h-convex, Godunova-Levin s-convex, s-convex in the 2^nd kind and hence contains class of convex. It also contains class of P-convex and class of Godunova-Levin functions. In this way we also capture the results with respect to convexity of functions.