Results 11 to 20 of about 169,237 (207)

Uniformly starlike functions and uniformly convex functions related to the Pascal distribution

Mathematica Bohemica, 2020
Summary: In this article, we aim to find sufficient conditions for a convolution of analytic univalent functions and the Pascal distribution series to belong to the families of uniformly starlike functions and uniformly convex functions in the open unit disk \(\mathbb{U}\). We also state corollaries of our main results.
Yalçın Tokgöz, Sibel, Murugusundaramoorthy, Gangadharan   +1 more
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Uniformly Alpha-Quasi-Convex Functions Defined by Janowski Functions [PDF]

Journal of Function Spaces, 2018
In this work, we aim to introduce and study a new subclass of analytic functions related to the oval and petal type domain. This includes various interesting properties such as integral representation, sufficiency criteria, inclusion results, and the convolution properties for newly introduced class.
Shahid Mahmood, Sarfraz Nawaz Malik, Sumbal Farman, S. M. Jawwad Riaz, Shabieh Farwa   +4 more
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On uniformly convex functions [PDF]

Annales Polonici Mathematici, 1991
The author introduces the class \(UCV\) of uniformly convex functions which consists of those convex functions \(f\) transforming any circular arc in the unit disk \(E\) with center \(\zeta\in E\) into a convex arc. He shows that \(f\in UCV\) if and only if \[ 1+\hbox{Re}\left({f''(z) \over f'(z)}(z- \zeta)\right)\geq 0, \] for every pair \((z,\zeta ...
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Uniformly convex functions on Banach spaces [PDF]

Proceedings of the American Mathematical Society, 2008
[EN] Given a Banach space (X,k · k), we study the connection between uniformly convex functions f : X ¿ R bounded above by k · kp , and the existence of norms on X with moduli of convexity of power type. In particular, we show that there exists a uniformly convex function f : X ¿ R bounded above by k · k2 if and only if X admits an equivalent norm with
Borwein, Jonathan M., Guirao, A. J., Hájek, P., Vanderwerff, J.   +3 more
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Compensated convexity methods for approximations and interpolations of sampled functions in Euclidean spaces: theoretical foundations [PDF]

, 2016
We introduce Lipschitz continuous and C¹,¹ geometric approximation and interpolation methods for sampled bounded uniformly continuous functions over compact sets and over complements of bounded open sets in Rn by using compensated convex transforms ...
Andreu F., Antonio Orlando, Attouch H., Clarke F. H., Elaine Crooks, Giaquinta M., Guichard F., Kewei Zhang, Moreau J.-J., Parikh N., Rockafellar R. T., van den Boomgaard R.   +11 more
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Non-Lipschitz minimizers of smooth uniformly convex functionals [PDF]

Proceedings of the National Academy of Sciences, 2002
We construct non-Lipschitz minimizers of smooth, uniformly convex functionals of type I ( u ) = ∫ Ω f ( Du ( x )) dx. Our method is based on the use of null Lagrangians.
Sverák, Vladimír, Yan, Xiaodong
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Moving energies as first integrals of nonholonomic systems with affine constraints [PDF]

, 2018
In nonholonomic mechanical systems with constraints that are affine (linear nonhomogeneous) functions of the velocities, the energy is typically not a first integral.
Fassò, Francesco, García-Naranjo, Luis C., Sansonetto, Nicola   +2 more
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An Extension Theorem for convex functions of class C1,1 on Hilbert spaces [PDF]

, 2017
Let H be a Hilbert space, E⊂H be an arbitrary subset and f:E→R, G:E→H be two functions. We give a necessary and sufficient condition on the pair (f,G) for the existence of a convex function F∈C1,1(H) such that F=f and ∇F=G on E.
Azagra Rueda, Daniel, Mudarra, C.
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Uniformly Convex and Uniformly Starlike Functions

, 2011
A normalized univalent function is uniformly convex if it maps every circular arc contained in the open unit disk with center in it into a convex curve. This article surveys recent results on the class of uniformly convex functions and on an analogous class of uniformly starlike functions.
Ali, R. M., Ravichandran, V.
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Classes of uniformly starlike and convex functions [PDF]

International Journal of Mathematics and Mathematical Sciences, 2004
Some classes of uniformly starlike and convex functions are introduced. The geometrical properties of these classes and their behavior under certain integral operators are investigated.
Saeid Shams, S. R. Kulkarni, Jay M. Jahangiri   +2 more
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