Abstract
In this paper, we prove some integral-norm inequalities for the polar derivative of lacunary-type complex polynomials having zeros in closed exterior or closed interior of a circle. The results obtained besides derive polar derivative analogues of some classical Bernstein and Tur?n-type inequalities for the uniform-norm also include several interesting generalizations and refinements of some integral-norm inequalities for polynomials as well.
Highlights
The use of non-symmetric basic tensor and non-symmetric connection starts to be actual specially in relation with the works of A
Eisenhart [4], a generalized Riemannian space (GRN ) is a differentiable manifold endowed with non-symmetric basic tensor
Mincic [10], [11], [14], 12 curvature tensors are obtained in GRN, and in S
Summary
The use of non-symmetric basic tensor and non-symmetric connection starts to be actual specially in relation with the works of A. Mincic [13] gave geometric interpretation of the torsion, curvature tensors and curvature pseudotensors of non-symmetric connection. P. Eisenhart [4], a generalized Riemannian space (GRN ) is a differentiable manifold endowed with non-symmetric basic tensor. Non-symmetric affine connection, generalized Riemannian space, independent curvature tensor, conformal transformation, invariants. Mincic [10], [11], [14], 12 curvature tensors are obtained in GRN , and in S. The cited independent curvature tensors in GRN are according to [12]:. A = Γijn;m, B = ΓpjnΓipm, where with ; n the covariant derivative on xn with respect to symmetric connection Γijk is denoted. Conformal transformation in GRN is transformation where basic tensor gij is changed by help of the rule
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