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Abstract. In this paper we establish variant inequalities of Ostrowski's type for functions whose derivatives in absolute value are m-convex and (α, m)-convex. Applications to some special means are obtained.

Shabir et. al [27] and D. N. Georgiou et. al [7], defined and studied some soft separation axioms, soft θ-continuity and soft connectedness in soft spaces using (ordinary) points of a topological space X. In this paper, we redefine and explore several properties of soft Ti, i = 0, 1, 2, soft regular, soft T3, soft normal and soft T4 axioms using soft points defined by I. Zorlutuna [30]. We also discuss some soft invariance properties namely soft topological property and soft hereditary property. We hope that these results will be useful for the future study on soft topology to carry out general framework for the practical applications and to solve the complicated problems containing uncertainties in economics, engineering, medical, environment and in general man-machine systems of various types.

In the present paper, we aim to prove a new lemma and quantum Simpson’s type inequalities for functions of two variables having convexity on co-ordinates over [ α , β ] × [ ψ , ϕ ] . Moreover, our deduction introduce new direction as well as validate the previous results.