Averaging operators and the classes of starlike functions related to parabola

Sokół, Janusz; Wiśniowska-Wajnryb, Agnieszka

doi:10.1007/s13324-019-00351-5

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Theorem 1 E Function λ(ω) � (ω/1 − Aω) Is In the Class1

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2023

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Cited by 6 publications

(1 citation statement)

References 11 publications

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“…e right-hand side of the above inequality (16), is seen to have minimum for θ � π and minimum value is (1 − r/2r + 1). Hence, a necessary and sufficient conditions for (16)…”

Section: Theorem 1 E Function λ(ω) � (ω/1 − Aω) Is In the Classmentioning

confidence: 84%

Analytic Functions Related with Starlikeness

Shah

Noor

Hussain

et al. 2021

Mathematical Problems in Engineering

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show abstract

“…e right-hand side of the above inequality (16), is seen to have minimum for θ � π and minimum value is (1 − r/2r + 1). Hence, a necessary and sufficient conditions for (16)…”

Section: Theorem 1 E Function λ(ω) � (ω/1 − Aω) Is In the Classmentioning

confidence: 84%

Analytic Functions Related with Starlikeness

Shah

Noor

Hussain

et al. 2021

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

Variable Hardy Spaces on Non-tangentially Accessible Domains and Their Applications to Div-Curl Lemma

2022

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A generalized integrable lattice hierarchy related to the Ablowitz–Ladik lattice: Conservation law, Darboux transformation and exact solution

Fan,

Xie

2023

Rev. Math. Phys.

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Under investigation in this paper is a more general discrete [Formula: see text] matrix spectral problem. Starting from this spectral problem, the positive and negative integrable lattice hierarchies are constructed based on the Tu scheme, then by considering linear combination of the positive and negative lattice hierarchies, we give a more general integrable lattice hierarchy, which can reduce to the well-known Ablowitz–Ladik lattice and the discrete modified Korteweg–de Vries (mKdV) equation. In particular, we obtain some local and nonlocal integrable lattice equations, including reverse-space discrete mKdV equation, reverse-space complex discrete mKdV equation, higher-order discrete mKdV equation, higher-order complex discrete mKdV equation, higher-order reverse-space discrete mKdV equation and higher-order reverse-space complex discrete mKdV equation. In additional, infinitely many conservation laws and Darboux transformation (DT) for the first non-trivial system in the hierarchy are established with the help of its Lax pair. The exact solutions of the system are generated by applying the obtained DT. The results in this paper might be helpful for understanding some physical phenomena.

show abstract

Averaging operators and the classes of starlike functions related to parabola

Cited by 6 publications

References 11 publications

Analytic Functions Related with Starlikeness

Analytic Functions Related with Starlikeness

Variable Hardy Spaces on Non-tangentially Accessible Domains and Their Applications to Div-Curl Lemma

A generalized integrable lattice hierarchy related to the Ablowitz–Ladik lattice: Conservation law, Darboux transformation and exact solution

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