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We introduce new subclasses S σ,s k λ, δ, φ and K σ,s k λ, δ, φ of analytic functions with respect to k-symmetric points defined by differential operator. Some interesting properties for these classes are obtained.

Motivated by Carlson-Shaffer linear operator, we define here a new generalized linear operator. Using this operator, we define a class of analytic functions in the unit disk U. For this class, a majorization problem of analytic functions is discussed.

In this work, we obtain some results for first order linear strong differential subordination for new subclass of generalized operator.

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