Results 1 to 10 of about 1,628,973 (292)
Conic regions and k -uniform convexity
Journal of Computational and Applied Mathematics, 1999 Let \(f(z)=z+a_2z^2+\dots\) be analytic and univalent in the unit disk \(D\). A function \(f\) is said to be \(k\)-uniformly convex in \(U\) if the image of every circular arc \(\gamma\), \(\gamma\subset D\) with its center at \(a\), \(|a|\leq k\), \(0\leq ...
S. Kanas, A. Wiśniowska
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Modular uniform convexity structures and applications to boundary value problems with non-standard growth [PDF]
Journal of Mathematical Analysis and Applications, 2023 We establish the existence and uniqueness of the solution to the Dirichlet problem for the variable exponent $p$-Laplacian on a bounded, smooth domain $\Omega \subset {\mathbb R}^n$, where the boundary datum belongs to $W^{1,p}(\Omega)$.
M. Khamsi, O. Méndez
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Strict Convexity and Uniform Convexity in Linear 2-normed Spaces
Journal of Harbin University of Science and Technology, 2021 Linear 2-normed space is a generalization of linear normed space, which defines a more extensive norm. In this paper, we get contraction mapping theorem in linear 2-normed space holds, and the set of fixed points for nonexpansive mapping is convex when ...
LI Shan-shan, CUI Yun-an
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Uniform Convexity in Variable Exponent Sobolev Spaces
Symmetry, 2023 We prove the modular convexity of the mixed norm Lp(ℓ2) on the Sobolev space W1,p(Ω) in a domain Ω⊂Rn under the sole assumption that the exponent p(x) is bounded away from 1, i.e., we include the case supx∈Ωp(x)=∞.
M. Bachar, M. Khamsi, O. Méndez
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Journal of Function Spaces, 2022 In this paper, we determine the radius of λ-uniform convexity, λ-starlikeness, and α-convexity of order δ for the Weierstrass canonical product of an entire function as a root having smallest modulus and argument ϕ of a functional equation.
K. A. Selvakumaran +3 more
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Some Aspects of Geometric Constants in Modular Spaces
European Journal of Mathematical Analysis, 2021 In this paper, we generalize the typical geometric constants of Banach spaces to modular spaces. We study the equivalence between the convexity of modular and normed spaces, and obtain the relationship between ρ-Neumann-Jordan constant and ρ-James ...
Zhijian Yang +3 more
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Certain Geometric Properties of the Fox–Wright Functions
Axioms, 2022 The primary objective of this study is to establish necessary conditions so that the normalized Fox–Wright functions possess certain geometric properties, such as convexity and pre-starlikeness.
Anish Kumar +2 more
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Geometric Properties and Hardy Spaces of Rabotnov Fractional Exponential Functions
Fractal and Fractional, 2023 The aim of this study is to investigate a certain sufficiency criterion for uniform convexity, strong starlikeness, and strong convexity of Rabtonov fractional exponential functions. We also study the starlikeness and convexity of order γ.
Mohsan Raza +5 more
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Modular Uniform Convexity in Every Direction in Lp(·) and Its Applications
Mathematics, 2020 We prove that the Lebesgue space of variable exponent L p ( · ) ( Ω ) is modularly uniformly convex in every direction provided the exponent p is finite a.e. and different from 1 a.e.
Mostafa Bachar, Osvaldo Méndez
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Geodesic stability, the space of rays and uniform convexity in Mabuchi geometry [PDF]
, 2018 We establish the essentially optimal form of Donaldson's geodesic stability conjecture regarding existence of constant scalar curvature K\"ahler metrics.
Tam'as Darvas, Chinh H. Lu
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