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Journal articles on the topic 'K-uniformly convex function'

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Published: 2 June 2025

Last updated: 31 July 2025

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1

Panigrahi, T., and R. El-Ashwah. "Mapping properties of certain linear operator associated with hypergeometric functions." Boletim da Sociedade Paranaense de Matemática 39, no. 2 (2021): 223–36. http://dx.doi.org/10.5269/bspm.39670.

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The main object of the present paper is to nd some su¢ cient conditions in terms of hypergeometric inequalities so that the linear operator denoted by Ha;b;c : maps a certain subclass of close-to-convex function R (A;B) into subclasses of k-uniformly starlike and k-uniformly convex functions k 􀀀ST () and k 􀀀UCV() respectively. Further, we consider an integral operator and discuss its properties. Our results generalize some relevant results.

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2

E., E. Ali. "SOME INCLUSION PROPERTIES FOR CERTAIN K-UNIFORMLY SUBCLASSES OF ANALYTIC FUNCTIONS ASSOCIATED WITH WRIGHT FUNCTION." International Journal of Research - Granthaalayah 7, no. 9 (2019): 218–29. https://doi.org/10.5281/zenodo.3473005.

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A new operator n n n n f z z a z n n ( ) 4 ( ) ( ( 1) ) , 2 ( 1) 1 ( )               W    is introduced for functions of the form   n n n f z  z   a z  2 which are analytic in the open unit disk U  z C: z 1 . We introduce several inclusion properties of the new k-uniformly classes US ;k;   , UC;k; , UK;k; ,  and UK ;k; ,  of analytic functions defined by using the Wright function with the operator  W, and the main object of this paper is to investigate various inclusion relationships for these classes. In addition, we proved that a special pr

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3

Giles, J. R. "A distance function property implying differentiability." Bulletin of the Australian Mathematical Society 39, no. 1 (1989): 59–70. http://dx.doi.org/10.1017/s0004972700027982.

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In a real normed linear space X, properties of a non-empty closed set K are closely related to those of the distance function d which it generates. If X has a uniformly Gâteaux (uniformly Fréchet) differentiable norm, then d is Gâteaux (Fréchet) differentiable at x ∈ X/K if there exists an such thatand is Géteaux (Fréchet) differentiable on X / K if there exists a set P+(K) dense in X/K where such a limit is approached uniformly for all x ∈ P+(K). When X is complete this last property implies that K is convex.

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4

Smith, Patrick Adrian Neale. "Counterexamples to Smoothing Convex Functions." Canadian Mathematical Bulletin 29, no. 3 (1986): 308–13. http://dx.doi.org/10.4153/cmb-1986-047-5.

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AbstractGreene and Wu have shown that any continuous strongly convex function on a Riemannian manifold can be uniformly approximated by infinitely differentiable strongly convex functions. This result is not true if the word “strongly” is omitted; in this paper, we give examples of manifolds on which convex functions cannot be approximated by convex functions (k = 0, 1,2,...).

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5

Ramachandran, C., S. Annamalai, and Basem Frasin. "The q-difference operator associated with the multivalent function bounded by conical sections." Boletim da Sociedade Paranaense de Matemática 39, no. 1 (2021): 133–46. http://dx.doi.org/10.5269/bspm.32913.

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In this paper we obtain some inclusion relations of k - starlike functions, k - uniformly convex functions and quasi-convex functions. Furthermore, we obtain coe¢ cient bounds for some subclasses of fractional q-derivative multivalent functions together with generalized Ruscheweyh derivative.

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6

Vanitha, Lakshminarayanan, Chellakutti Ramachandran, and Teodor Bulboacă. "CLASSES OF k-UNIFORMLY CONVEX AND STARLIKE FUNCTIONS INVOLVING THE GENERALIZED FOX-WRIGHT FUNCTION." Far East Journal of Mathematical Sciences (FJMS) 99, no. 7 (2016): 1081–107. http://dx.doi.org/10.17654/ms099071081.

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7

Huffer, F. W., and L. A. Shepp. "On the probability of covering the circle by random arcs." Journal of Applied Probability 24, no. 2 (1987): 422–29. http://dx.doi.org/10.2307/3214266.

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Arcs of length lk, 0 < lk < 1, k = 1, 2, ···, n, are thrown independently and uniformly on a circumference having unit length. Let P(l1, l2, · ··, ln) be the probability that is completely covered by the n random arcs. We show that P(l1, l2,· ··, ln) is a Schur-convex function and that it is convex in each argument when the others are held fixed.

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8

Huffer, F. W., and L. A. Shepp. "On the probability of covering the circle by random arcs." Journal of Applied Probability 24, no. 02 (1987): 422–29. http://dx.doi.org/10.1017/s0021900200031065.

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Arcs of length lk, 0 &lt; lk &lt; 1, k = 1, 2, ···, n, are thrown independently and uniformly on a circumference having unit length. Let P(l 1 , l 2, · ··, ln ) be the probability that is completely covered by the n random arcs. We show that P(l 1 , l 2 ,· ··, ln ) is a Schur-convex function and that it is convex in each argument when the others are held fixed.

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9

Wong, James C. S. "Fixed Point Theorems for Measurable Semigroups of Operations." Canadian Journal of Mathematics 44, no. 3 (1992): 652–64. http://dx.doi.org/10.4153/cjm-1992-039-4.

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AbstractLet Sbe a topological semigroup, K a compact convex subset of a separated convex space Eand T: S x K → K an affine action (denoted by (s, x) → Ts(x),s ∈ S, x ∈ K) of S as continuous affine maps on K. It is shown in A. Lau and J. Wong [22] that the weakly left uniformly measurable functions WLUM(S) on S has a left invariant mean iff Shas the fixed point property for weakly measurable affine actions, i.e. affine actions such that the scalar function s → x*Ts(x) is measurable for each x ∈ K and x*∈ E* (the dual of E) with respect to the Borel sets in S. It is natural to ask for a “strongl

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10

Barber, B. C. "On the dispersion relation for trapped internal waves." Journal of Fluid Mechanics 252 (July 1993): 31–49. http://dx.doi.org/10.1017/s0022112093003659.

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An analysis is constructed in order to estimate the dispersion relation for internal waves trapped in a layer and propagating linearly in a fluid of infinite depth with a rigid surface. The main interest is in predicting the structure of internal wave wakes, but the results are applicable to any internal waves. It is demonstrated that, in general 1/cp = 1/CpO + k/ωmax + ∈(k) where cp is the wave phase speed for a particular mode, CpO is the phase speed at k = 0, ωmax is the maximum possible wave angular frequency and ωmax ≤ Nmax where Nmax is the maximum buoyancy frequency. Also, ∈(0) = 0, ∈(k

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11

Gangadharan, A., T. N. Shanmugam, and H. M. Srivastava. "Generalized hypergeometric functions associated with k-uniformly convex functions." Computers & Mathematics with Applications 44, no. 12 (2002): 1515–26. http://dx.doi.org/10.1016/s0898-1221(02)00275-4.

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12

Akbarally, Ajab, and Maslina Darus. "Applications of fractional calculus to $ k $-uniformly starlike and $ k $-uniformly convex functions of order $ \alpha $." Tamkang Journal of Mathematics 38, no. 2 (2007): 103–9. http://dx.doi.org/10.5556/j.tkjm.38.2007.81.

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A new subclass of analytic functions $ k-SP_\lambda(\alpha) $ is introduced by applying certain operators of fractional calculus to $k$-uniformly starlike and $ k $-uniformly convex functions of order $ \alpha $. Some theorems on coefficient bounds and growth and distortion theorems for this subclass are found. The radii of close to convexity, starlikeness and convexity for this subclass is also derived.

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13

Li, Shuhai, Huo Tang, Lina Ma, and Ao En. "Generalized k–uniformly convex harmonic functions with negative coefficients." Tamkang Journal of Mathematics 48, no. 2 (2017): 185–202. http://dx.doi.org/10.5556/j.tkjm.48.2017.2326.

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In the present paper, we introduce some generalized $k$-uniformly convex harmonic functions with negative coefficients. Sufficient coefficient conditions, distortion bounds, extreme points, Hadamard product and partial sum for functions of these classes are obtained.

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14

Aqlan, Essam, Jay M. Jahangiri, and S. R. Kulkarni. "New classes of $k$-uniformly convex and starlike functions." Tamkang Journal of Mathematics 35, no. 3 (2004): 261–66. http://dx.doi.org/10.5556/j.tkjm.35.2004.207.

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Certain classes of analytic functions are defined which will generalize new, as well as well-known, classes of k-uniformly convex and starlike functions. We provide necessary and sufficent coefficient conditions, distortion bounds, extreme points and radius of starlikeness for these classes.

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15

Porwal, Saurabh, Poonam Dixit, Ritesh Agarwal, and Akhilesh Singh. "UNIFORMLY CONVEX AND STARLIKE PROBABILITY DISTRIBUTION." South East Asian J. of Mathematics and Mathematical Sciences 19, no. 03 (2023): 481–92. http://dx.doi.org/10.56827/seajmms.2023.1903.37.

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The purpose of the present paper is to introduce k− uniformly convex and k− uniformly starlike discrete probability distributions and obtain some results regarding moments, factorial moments and moment generating functions for these distributions.

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16

Noor, Khalida Inayat, Mohammad Arif, and Wasim Ul-Haq. "On k-uniformly close-to-convex functions of complex order." Applied Mathematics and Computation 215, no. 2 (2009): 629–35. http://dx.doi.org/10.1016/j.amc.2009.05.050.

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17

Seker, Bilal, Mugur Acu, and Sevtap Sumer Eker. "SUBCLASSES OF k-UNIFORMLY CONVEX AND k-STARLIKE FUNCTIONS DEFINED BY SĂLĂGEAN OPERATOR." Bulletin of the Korean Mathematical Society 48, no. 1 (2011): 169–82. http://dx.doi.org/10.4134/bkms.2011.48.1.169.

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18

Ali, Irfan, Yousaf Ali Khan Malghani, Sardar Muhammad Hussain, Nazar Khan, and Jong-Suk Ro. "Generalization of k-Uniformly Starlike and Convex Functions Using q-Difference Operator." Fractal and Fractional 6, no. 4 (2022): 216. http://dx.doi.org/10.3390/fractalfract6040216.

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In this article we have defined two new subclasses of analytic functions k−Sq[A,B] and k−Kq[A,B] by using q-difference operator in an open unit disk. Furthermore, the necessary and sufficient conditions along with certain other useful properties of these newly defined subclasses have been calculated by using q-difference operator.

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19

Bednarz, Urszula. "STABILITY OF THE HADAMARD PRODUCT OF k-UNIFORMLY CONVEX AND k-STARLIKE FUNCTIONS IN CERTAIN NEIGHBOURHOOD." Demonstratio Mathematica 38, no. 4 (2005): 837–46. http://dx.doi.org/10.1515/dema-2005-0407.

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20

Kanas, Stanisława. "Norm of pre-Schwarzian derivative for the class of k-uniformly convex and k-starlike functions." Applied Mathematics and Computation 215, no. 6 (2009): 2275–82. http://dx.doi.org/10.1016/j.amc.2009.08.021.

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21

Gupta, Purvi, and Rasul Shafikov. "Polynomially convex embeddings of odd-dimensional closed manifolds." Journal für die reine und angewandte Mathematik (Crelles Journal) 2021, no. 777 (2021): 273–99. http://dx.doi.org/10.1515/crelle-2021-0021.

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Abstract It is shown that any smooth closed orientable manifold of dimension 2 ⁢ k + 1 {2k+1} , k ≥ 2 {k\geq 2} , admits a smooth polynomially convex embedding into ℂ 3 ⁢ k {\mathbb{C}^{3k}} . This improves by 1 the previously known lower bound of 3 ⁢ k + 1 {3k+1} on the possible ambient complex dimension for such embeddings (which is sharp when k = 1 {k=1} ). It is further shown that the embeddings produced have the property that all continuous functions on the image can be uniformly approximated by holomorphic polynomials. Lastly, the same technique is modified to construct embeddings whose

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22

Ramachandran, C., T. N. Shanmugam, H. M. Srivastava, and A. Swaminathan. "A unified class of k-uniformly convex functions defined by the Dziok–Srivastava linear operator." Applied Mathematics and Computation 190, no. 2 (2007): 1627–36. http://dx.doi.org/10.1016/j.amc.2007.02.042.

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23

Amsheri, Somia, and Valentina Zharkova. "Certain Subclass of k-Uniformly p-Valent Starlike and Convex Functions Associated with Fractional Derivative Operators." British Journal of Mathematics & Computer Science 2, no. 4 (2012): 242–54. http://dx.doi.org/10.9734/bjmcs/2012/1352.

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24

Salah, Jamal, Hameed Ur Rehman, and Iman Al Buwaiqi. "Inclusion Results of a Generalized Mittag-Leffler-Type Poisson Distribution in the k-Uniformly Janowski Starlike and the k-Janowski Convex Functions." Mathematics and Statistics 11, no. 1 (2023): 22–27. http://dx.doi.org/10.13189/ms.2023.110103.

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25

Mishra, A. K., and P. Gochhayat. "The Fekete–Szegö problem for k-uniformly convex functions and for a class defined by the Owa–Srivastava operator." Journal of Mathematical Analysis and Applications 347, no. 2 (2008): 563–72. http://dx.doi.org/10.1016/j.jmaa.2008.06.009.

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26

AOUF, MOHAMED KAMAL, NANJUNDAN MAGESH та JAGADESAN YAMINI. "Certain Subclasses of k-Uniformly Starlike and Convex Functions of Order α and Type β with Varying Argument Coefficients". Kyungpook mathematical journal 55, № 2 (2015): 383–94. http://dx.doi.org/10.5666/kmj.2015.55.2.383.

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27

Amsheri, Somia Muftah, and Valentina Zharkova. "Certain Subclass of k-Uniformly p-Valent Starlike and Convex Functions Associated with Fractional Derivative Operators." December 8, 2012. https://doi.org/10.5281/zenodo.9015.

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In this paper, we introduce a new subclass k 􀀀 UCV ;;br /> ;br /> ; (p; ) of k-uniformly p-valent starlike andbr /> convex functions in the open unit disk using a fractional differential operator. We obtain coefficientbr /> estimates, distortion theorems, extermal properties, closure theorems, and inclusion properties.br /> The radii for k-uniformly starlikeness, convexity and close-to-convexity for functions belonging tobr /> this class are also determined./p> p>Note: Due to technical problem the abstract was not uploaded properly. Kindly see the PDF copy for the corre

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28

Doikov, Nikita, and Yurii Nesterov. "Gradient regularization of Newton method with Bregman distances." Mathematical Programming, March 24, 2023. http://dx.doi.org/10.1007/s10107-023-01943-7.

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AbstractIn this paper, we propose a first second-order scheme based on arbitrary non-Euclidean norms, incorporated by Bregman distances. They are introduced directly in the Newton iterate with regularization parameter proportional to the square root of the norm of the current gradient. For the basic scheme, as applied to the composite convex optimization problem, we establish the global convergence rate of the order $$O(k^{-2})$$ O ( k - 2 ) both in terms of the functional residual and in the norm of subgradients. Our main assumption on the smooth part of the objective is Lipschitz continuity

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29

Kolasiński, Sławomir, and Mario Santilli. "Regularity of the distance function from arbitrary closed sets." Mathematische Annalen, May 16, 2022. http://dx.doi.org/10.1007/s00208-022-02407-7.

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AbstractWe investigate the distance function $$\varvec{\delta }_{K}^{\phi }$$ δ K ϕ from an arbitrary closed subset K of a finite-dimensional Banach space $$ (\mathbf {R}^{n}, \phi ) $$ ( R n , ϕ ) , equipped with a uniformly convex $$ \mathscr {C}^{2} $$ C 2 -norm $$ \phi $$ ϕ . These spaces are known as Minkowski spaces and they are one of the fundamental spaces of Finslerian geometry (see Martini et al. in Expo Math 19:97–142, 2001, 10.1016/S0723-0869(01)80025-6). We prove that the gradient of $$\varvec{\delta }_{K}^{\phi }$$ δ K ϕ satisfies a Lipschitz property on the complement of the $$\

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30

Lee, Han Ju, and Hyung-Joon Tag. "Remark on the Daugavet property for complex Banach spaces." Demonstratio Mathematica 57, no. 1 (2024). http://dx.doi.org/10.1515/dema-2024-0004.

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Abstract In this article, we study the Daugavet property and the diametral diameter two properties (DD2Ps) in complex Banach spaces. The characterizations for both Daugavet and Δ \Delta -points are revisited in the context of complex Banach spaces. We also provide relationships between some variants of alternative convexity and smoothness, nonsquareness, and the Daugavet property. As a consequence, every strongly locally uniformly alternatively convex or smooth (sluacs) Banach space does not contain Δ \Delta -points from the fact that such spaces are locally uniformly nonsquare. We also study

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31

Narayanan, Hariharan, Amit Rajaraman, and Piyush Srivastava. "Sampling from convex sets with a cold start using multiscale decompositions." Probability Theory and Related Fields, December 13, 2024. https://doi.org/10.1007/s00440-024-01341-w.

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AbstractA standard approach for sampling approximately uniformly from a convex body $$K \subseteq \mathbb {R}^n$$ K ⊆ R n is to run a random walk within K. The requirement is that starting from a suitable initial distribution, the random walk should “mix rapidly”, i.e., after a number of steps that is polynomial in n and the aspect ratio R/r (here, K is assumed to contain a ball of radius r and to be contained within a ball of radius R), the distribution of the random walk should come close to the uniform distribution $$\pi _K$$ π K on K. Different random walks differ in aspects such as the ea

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32

Kohlenbach, Ulrich. "Effective Uniform Bounds on the Krasnoselski-Mann Iteration." BRICS Report Series 7, no. 9 (2000). http://dx.doi.org/10.7146/brics.v7i9.20136.

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This paper is a case study in proof mining applied to non-effective proofs<br />in nonlinear functional analysis. More specifically, we are concerned with the<br />fixed point theory of nonexpansive selfmappings f of convex sets C in normed spaces. We study the Krasnoselski iteration as well as more general so-called Krasnoselski-Mann iterations. These iterations converge to fixed points of f only under special compactness conditions and even for uniformly convex<br />spaces the rate of convergence is in general not computable in f (which is<br />related to the non-uniq

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33

Bednarz, U., and S. Kanas. "Stability of the Integral Convolution of k-Uniformly Convex and k-Starlike Functions." Journal of Applied Analysis 10, no. 1 (2004). http://dx.doi.org/10.1515/jaa.2004.105.

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34

"On Generalized k-Uniformly Close-to-Convex Functions of Janowski Type." International Journal of Analysis and Applications, 2019. http://dx.doi.org/10.28924/2291-8639-17-2019-958.

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35

Shanmugam, T. N., S. Sivasubramanian, and M. Darus. "On a subclass of k-uniformly convex functions with negative coefficients." International Mathematical Forum, 2006, 1677–89. http://dx.doi.org/10.12988/imf.2006.06144.

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36

Zhou, Wen-Han, and Patrick Michel. "A semi-analytical thermal model for craters with application to the crater-induced YORP effect." Astronomy & Astrophysics, December 15, 2023. http://dx.doi.org/10.1051/0004-6361/202346970.

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The YORP effect is the thermal torque generated by radiation from the surface of an asteroid. The effect is sensitive to surface topology, including small-scale roughness, boulders, and craters. The aim of this paper is to develop a computationally efficient semi-analytical model for the crater-induced YORP (CYORP) effect that can be used to investigate the functional dependence of this effect. This study linearizes the thermal radiation term as a function of the temperature in the boundary condition of the heat conductivity, and obtains the temperature field in a crater over a rotational peri

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37

Amini, Ebrahim, and Shrideh Al-Omari. "On k-uniformly starlike convex functions associated with (j, m)-ply symmetric points." Afrika Matematika 36, no. 1 (2025). https://doi.org/10.1007/s13370-025-01254-4.

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38

Yaşar, Elif, and Sibel Yalçin. "Neighbourhoods of two new classes of harmonic univalent functions with varying arguments." Mathematica Slovaca 64, no. 6 (2014). http://dx.doi.org/10.2478/s12175-014-0283-x.

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AbstractIn this paper, two new classes of harmonic univalent functions with varying arguments are defined by using planar harmonic convolution operator involving hypergeometric functions. Those classes are of special interest because they contain various classes of well-known harmonic univalent functions such as the classes of k-starlike and k-uniformly convex harmonic univalent functions. The main purpose of this paper is to investigate neighbourhoods of the classes in question.

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39

Lowy, Andrew, and Meisam Razaviyayn. "Private Stochastic Optimization with Large Worst-Case Lipschitz Parameter." Journal of Privacy and Confidentiality 15, no. 1 (2025). https://doi.org/10.29012/jpc.909.

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We study differentially private (DP) stochastic optimization (SO) with loss functions whose worst-case Lipschitz parameter over all data points may be huge or infinite. To date, the most work on DP SO assumes that the loss is uniformly Lipschitz continuous over data (i.e. stochastic gradients are uniformly bounded over all data points). While this assumption is convenient, it often leads to pessimistic excess risk bounds. In practical problems, the worst-case Lipschitz parameter of the loss over all data points may be huge due to outliers and/or heavy-tailed data. In such cases, the error boun

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40

Gallenmüller, Dennis. "Müller–Zhang truncation for general linear constraints with first or second order potential." Calculus of Variations and Partial Differential Equations 60, no. 3 (2021). http://dx.doi.org/10.1007/s00526-021-01979-7.

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AbstractLet $$\mathcal {B}$$ B be a homogeneous differential operator of order $$l=1$$ l = 1 or $$l=2$$ l = 2 . We show that a sequence of functions of the form $$(\mathcal {B}u_j)_j$$ ( B u j ) j converging in the $$L^1$$ L 1 -sense to a compact, convex set K can be modified into a sequence converging uniformly to this set provided that the derivatives of order l are uniformly bounded. We prove versions of our result on the whole space, an open domain, and for K varying uniformly continuously on an open, bounded domain. This is a conditional generalization of a theorem proved by S. Müller for

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41

Noor, Khalida Inayat, Nasir Khan, Muhammad Arif, and Janusz Sokół. "On some subclasses k-uniformly Janowski starlike and convex functions associated with t-symmetric points." Hacettepe Journal of Mathematics and Statistics, December 31, 2019, 1–11. http://dx.doi.org/10.15672/hujms.588741.

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42

Malik, Faroze Ahmad, Nusrat Ahmed Dar, and Chitaranjan Sharma. "Certain Properties of a Generalized Class of Analytic Functions Involving Some Convolution Operator." Earthline Journal of Mathematical Sciences, May 28, 2021, 49–76. http://dx.doi.org/10.34198/ejms.7121.4976.

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We use the concept of convolution to introduce and study the properties of a unified family $\mathcal{TUM}_\gamma(g,b,k,\alpha)$, $(0\leq\gamma\leq1,\,k\geq0)$, consisting of uniformly $k$-starlike and $k$-convex functions of complex order $b\in\mathbb{C}\setminus\{0\}$ and type $\alpha\in[0,1)$. The family $\mathcal{TUM}_\gamma(g,b,k,\alpha)$ is a generalization of several other families of analytic functions available in literature. Apart from discussing the coefficient bounds, sharp radii estimates, extreme points and the subordination theorem for this family, we settle down the Silverman's

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43

Kabluchko, Zakhar. "Recursive Scheme for Angles of Random Simplices, and Applications to Random Polytopes." Discrete & Computational Geometry, December 10, 2020. http://dx.doi.org/10.1007/s00454-020-00259-z.

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AbstractConsider a random simplex $$[X_1,\ldots ,X_n]$$ [ X 1 , … , X n ] defined as the convex hull of independent identically distributed (i.i.d.) random points $$X_1,\ldots ,X_n$$ X 1 , … , X n in $$\mathbb {R}^{n-1}$$ R n - 1 with the following beta density: "Equation missing" Let $$J_{n,k}(\beta )$$ J n , k ( β ) be the expected internal angle of the simplex $$[X_1,\ldots ,X_n]$$ [ X 1 , … , X n ] at its face $$[X_1,\ldots ,X_k]$$ [ X 1 , … , X k ] . Define $${\tilde{J}}_{n,k}(\beta )$$ J ~ n , k ( β ) analogously for i.i.d. random points distributed according to the beta$$'$$ ′ density $

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