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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]

The main object of this paper is to deduce the bibasic Humbert functions Ξ1 and Ξ2 Some interesting results and elementary summations technique that was successfully employed, q–recursion, q–derivatives relations, the q–differential recursion relations, the q–integral representations for Ξ1 and Ξ2 are given. The summation formula derives a list of p–analogues of transformation formulas for bibasic Humbert functions that have been studied, also some hypergeometric functions properties of some new interesting special cases have been given. [ABSTRACT FROM AUTHOR]

In this article, we introduce Stancu-type modification of generalized Baskakov-Szász operators. We obtain recurrence relations to calculate moments for these new operators. We study several approximation properties and q -statistical approximation for these operators. [ABSTRACT FROM AUTHOR]