Authors:
Vu Nhat HuyDepartment of Mathematics, Hanoi University of Science, Vietnam National University 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam
Thang Long Institute of Mathematics and Applied Sciences, Thang Long University

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Nguyen Ngoc HuyDepartment of Mathematics, Thuyloi University 175 Tay Son, Dong Da, Hanoi, Vietnam

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Chu Van TiepDepartment of Mathematics, The University of Danang - University of Science and Education 459 Ton Duc Thang, Danang, Vietnam

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In this paper, we establish some Landau–Kolmogorov type inequalities for differential operators generated by polynomials in the following form
P ( D ) f p K 1 ( ε , P ) f q + K 2 ( ε , m ) D m ( P ( D ) f ) p

for all ε > 0 , where 0 < gp ≤ ∞, and the differential operator P (D) is obtained from the polynomial P (x) by substituting x i / x . Moreover, the explicit form of K 1 ( ε , p ) and K 2 ( ε , m )

are given.

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Studia Scientiarum Mathematicarum Hungarica
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