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In this paper, we give some properties of the Dunkl–Gamma‐type operators including Appell polynomials, using into consideration the generalized power summability method. In the first section are given moments of the new defined operators. In second section are given some direct estimation related to the Dunkl–Gamma‐type operators, including Korovkin‐type theorem. In the third section, we give some results related to the weighted spaces of continuous functions, and in the last section, we give some properties in the sense of A$$ A $$‐statistically convergence, including Voronovskaya and Grüss–Voronovskaya‐type theorem. [ABSTRACT FROM AUTHOR]

In this paper, we establish a novel category of sequence spaces ℓ p q λ and ℓ ∞ q λ by utlizing q-analogue Λ q of Λ-matrix. Our investigation outlines several topological characteristics and inclusion results of these newly introduced sequence spaces, specifically identifying them as BK-spaces. Subsequently, we demonstrate that these novel sequence spaces are of nonabsolute type and establish their isometric isomorphism with ℓ p and ℓ ∞ . Moreover, we obtain the α-, β-, and γ-duals of these sequence spaces. We further characterize the class (ℓ p q λ , X) of matrices, where X is any of the spaces ℓ ∞ , c, or c 0 . Lastly, our study delves into the exploration of specific geometric properties exhibited by the space ℓ p q λ . [ABSTRACT FROM AUTHOR]

The main object of this paper is to construct a new class of modified (p , q) -Gamma-type operators. For this new class of operators, in section one, the general moments are find; in section two, the Korovkin-type theorem and some direct results are proved by considering the modulus of continuity and modulus of smoothness and their behavior in Lipschitz-type spaces. In section three, some results in the weighted spaces are given, and in the end, some shape-preserving properties are proven. [ABSTRACT FROM AUTHOR]

In this paper, we have construct a new version of the Bézier‐type Baskakov–Schurer–Szász–Stancu operators. For this new class of operators, uniform convergence is shown in any compact subset or positive real line. We prove Korovkin‐type theorem, Voronovskaya‐type theorem, and Grüss–Voronovskaya‐type theorem. Moreover, at the end, we express the behavior of the operators in the Lipschitz‐type space using the modulus of continuity and smoothness. [ABSTRACT FROM AUTHOR]