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In this article, we use the notion of lacunary statistical convergence of order (α,β)\left(\alpha ,\beta ) to introduce new sequence spaces by lacunary sequence, invariant means defined by Musielak-Orlicz function ℳ=(ℵk){\mathcal{ {\mathcal M} }}=\left({\aleph }_{k}). We also examine some topological properties and prove inclusion relations between newly constructed sequence spaces.

In this study, a different generalization of q-Bernstein operators with the parameter λ ∈ [ − 1 , 1 ] is created. The moments and central moments of these operators are calculated, a statistical approximation result for this new type of (λ , q) -Bernstein operators is obtained, and the convergence properties are analyzed using the Peetre K-functional and the modulus of continuity for this new operator. Finally, a numerical example is given to illustrate the convergence behavior of the newly defined operators. [ABSTRACT FROM AUTHOR]