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Mechanics of Materials, ISSN 0167-6636, 11/2017, Volume 114, pp. 107 - 118
•Concavity-convexity transition phenomenon of loading curve for spherical indentation was found... 
Spherical indentation | Concavity-convexity transition | Loading curve | Deformation patterns | MECHANICS | MODULUS | MATERIALS SCIENCE, MULTIDISCIPLINARY | PARAMETERS | STRESS | ELASTIC-PLASTIC SOLIDS | INDENTER
Journal Article
Demonstratio Mathematica, ISSN 0420-1213, 05/2018, Volume 51, Issue 1, pp. 85 - 105
Here we search quantitatively under convexity the approximation of multivariate function by general multivariate positive sublinear operators with applications to multivariate Max-product operators... 
multivariate positive sublinear operators | 41A25 | 41A36 | 41A63 | multivariate modulus of continuity | multivariate Max-product operators | convexity | 41A17 | Multivariate positive sublinear operators | Multivariate Max-product operators | Convexity | Multivariate modulus of continuity
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2009, Volume 360, Issue 1, pp. 307 - 316
.... We consider the situation in infinite-dimensional uniformly convex Banach spaces. We use the notion of Polyak of uniform convexity and modulus of uniform convexity for arbitrary convex sets (not necessary balls... 
Uniformly continuous selection | Modulus of convexity | Reflexive Banach space | Set-valued mapping | Splitting problem | Uniform convexity | MATHEMATICS | MATHEMATICS, APPLIED | Universities and colleges
Journal Article
Acta Mathematica Hungarica, ISSN 0236-5294, 2/2011, Volume 130, Issue 3, pp. 254 - 285
...Acta Math. Hungar., 130 (3) (2011), 254–285 DOI: 10.1007/s10474-010-0008-8 First published online November 3, 2010 CONVEXITY, MODULI OF SMOOTHNESS... 
41A25 | 41A63 | L p space | 46B20 | Mathematics, general | Mathematics | Orlicz space | modulus of smoothness | 47D60 | Jackson inequality | 41A17 | space | MATHEMATICS | AVERAGES | MARCHAUD | APPROXIMATION | SPACES | L-p space | SPHERE | CONVERSE INEQUALITIES | Equality | Mathematics - Classical Analysis and ODEs
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2010, Volume 371, Issue 2, pp. 407 - 413
Let X and Y be Banach spaces and T : Y → X be a bounded operator. In this note, we show first some operator versions of the dual relation between q-convexity and p-smoothness of Banach spaces case... 
Modulus of convexity | p-Convexity of operators | Convexity | Banach space | Smoothness | P-Convexity of operators | MATHEMATICS | MATHEMATICS, APPLIED | BANACH-SPACES | MARTINGALE TYPE | UNIFORMLY CONVEX
Journal Article
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2006, Volume 320, Issue 2, pp. 543 - 548
In this paper, we prove that the moduli of W ∗ -convexity, introduced by Ji Gao [J. Gao, The W ∗ -convexity and normal structure in Banach spaces, Appl... 
Super-reflexive space | Uniform normal structure | Modulus of [formula omitted]-convexity | Modulus of W | convexity | MATHEMATICS | super-reflexive space | MATHEMATICS, APPLIED | modulus of W-convexity | uniform normal structure | BANACH-SPACES
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 11/2013, Volume 91, pp. 60 - 71
According to a result due to B.T. Polyak, a mapping between Hilbert spaces, which is C1,1 around a regular point, carries a ball centered at that point to a... 
Lagrangian duality | Value function | Modulus of convexity | [formula omitted] mapping | Metric regularity | Uniformly convex Banach space | Constrained optimization | mapping | Banach space | Uniformly convex | MATHEMATICS | MATHEMATICS, APPLIED | C-1,C-1 mapping | Constraints | Mathematical analysis | Nonlinearity | Mapping | Variational principles | Localization | Optimization
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2008, Volume 344, Issue 2, pp. 851 - 856
We prove that F-convexity, the property dual to P-convexity of Kottman, implies uniform normal structure... 
P-convexity | E-convexity | Normal structure | F-convexity | WORTH property | O-convexity | MATHEMATICS, APPLIED | MODULUS | NEUMANN-JORDAN CONSTANT | normal structure | UNIFORM NORMAL STRUCTURE | MATHEMATICS | MAPPINGS | FIXED-POINT PROPERTY | LINEAR-SPACES
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2011, Volume 377, Issue 2, pp. 754 - 761
We prove that in the Hilbert space every uniformly convex set with modulus of convexity of the second order at zero is an intersection of closed balls of fixed radius... 
Set-valued mapping | Supporting function | Modulus of convexity | Generating set | Hilbert space | Strongly convex set of radius R | Uniform convexity | MATHEMATICS | MATHEMATICS, APPLIED | SETS | Electric generators | Universities and colleges
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 10/2007, Volume 135, Issue 10, pp. 3233 - 3240
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2005, Volume 307, Issue 1, pp. 86 - 101
Journal Article
Central European Journal of Mathematics, ISSN 1895-1074, 12/2012, Volume 10, Issue 6, pp. 2264 - 2271
We find conditions for a smooth nonlinear map f: U → V between open subsets of Hilbert or Banach spaces to be locally convex in the sense that for some c and... 
52A41 | Topological Groups, Lie Groups | 46B20 | Probability Theory and Stochastic Processes | Lipschitzopen maps | Mathematics | Locally convex mapping | Modulus of smoothness | Geometry | Algebra | Hilbert and Banach spaces | 49J50 | Mathematics, general | Modulus of convexity | Number Theory | 58C20 | MATHEMATICS | Lipschitz-open maps | SMOOTHNESS | THEOREM | MODULI
Journal Article
Annals of Functional Analysis, ISSN 2008-8752, 2012, Volume 3, Issue 1, pp. 1 - 9
It is well known that different kinds of expressions of modulus of convexity are essentially based on two geometrical propositions... 
Modulus of convexity | Hahn-Banach theorem | Normed spaces | normed spaces | MATHEMATICS | MATHEMATICS, APPLIED | modulus of convexity
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2013, Volume 400, Issue 2, pp. 743 - 750
Strongly convex sets in Hilbert spaces are characterized by local properties. One quantity which is used for this purpose is a generalization of the modulus of convexity δΩ of a set Ω... 
Strongly convex set | Modulus of convexity | Hilbert space | Convexity | Strong convexity | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Quaestiones Mathematicae, ISSN 1607-3606, 09/2009, Volume 32, Issue 3, pp. 307 - 319
We provide some properties of both moduli of convexity δ and β and derive some applications of the modulus β... 
Modulus of convexity | fixed point property | Banach Mazur-distance | FIXED POINT PROPERTY | BANACH MAZUR-DISTANCE | MODULUS OF CONVEXITY | Fixed point property | MATHEMATICS | SMOOTHNESS
Journal Article
Journal of Computational Analysis and Applications, ISSN 1521-1398, 10/2020, Volume 28, Issue 5, pp. 848 - 860
Journal Article
Journal of Fixed Point Theory and Applications, ISSN 1661-7738, 6/2018, Volume 20, Issue 2, pp. 1 - 10
Journal Article
by Gao, J
Applied Mathematics Letters, ISSN 0893-9659, 2003, Volume 16, Issue 3, pp. 273 - 278
.... Let δ(ϵ) = inf{1 − ‖x + y‖ 2 : ‖x − y‖ ≤ ϵ} , where x, y ϵ S( X 2) and 0 ≤ ϵ ≤ 2 is the modulus of convexity of X... 
Modulus of convexity | Normal structure | Uniformly nonsquare space | Arc length | Uniform normal structure | ultraproduct space | MATHEMATICS, APPLIED | uniform normal structure and ultraproduct space | arc length | uniformly nonsquare space | modulus of convexity | normal structure
Journal Article
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