scholarly journals Smooth approximation of convex functions in Banach spaces

2006 ◽  
Vol 313 (2) ◽  
pp. 572-580 ◽  
Author(s):  
Linxin Cheng ◽  
Shaoxiong Chen
Keyword(s):  
Banach Spaces ◽  
Convex Functions ◽  
Smooth Approximation

scholarly journals On weak Hadamard differentiability of convex functions on Banach spaces

1996 ◽  
Vol 54 (1) ◽  
pp. 155-166 ◽  
Author(s):  
J.R. Giles ◽  
Scott Sciffer
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Convex Functions ◽  
Directional Differentiability ◽  
Hadamard Differentiability ◽  
Hadamard Directional Differentiability

We study two variants of weak Hadamard differentiability of continuous convex functions on a Banach space, uniform weak Hadamard differentiability and weak Hadamard directional differentiability, and determine their special properties on Banach spaces which do not contain a subspace topologically isomorphic to l1.

scholarly journals Approximation of Convex Functions on the Dual of Banach Spaces

2002 ◽  
Vol 116 (1) ◽  
pp. 126-140 ◽  
Author(s):  
Lixin Cheng ◽  
Yingbin Ruan ◽  
Yanmei Teng
Keyword(s):  
Banach Spaces ◽  
Convex Functions

scholarly journals Higher order Gateaux smooth bump functions on Banach spaces

1995 ◽  
Vol 51 (2) ◽  
pp. 291-300 ◽  
Author(s):  
David P. McLaughlin ◽  
Jon D. Vanderwerff
Keyword(s):  
Banach Spaces ◽  
Higher Order ◽  
Smooth Approximation ◽  
Bump Function

For Г uncountable and p ≥ 1 odd, it is shown ℓp(г) admits no continuous p-times Gateaux differentiable bump function. A space is shown to admit a norm with Hölder derivative on its sphere if it admits a bounded bump function with uniformly directionally Hölder derivative. Some results on smooth approximation are obtained for spaces that admit bounded uniformly Gateaux differentiable bump functions.

scholarly journals NEAREST POINTS AND DELTA CONVEX FUNCTIONS IN BANACH SPACES

2015 ◽  
Vol 93 (2) ◽  
pp. 283-294
Author(s):  
JONATHAN M. BORWEIN ◽  
OHAD GILADI
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Convex Functions ◽  
Closed Set ◽  
Nearest Point ◽  
Set Of Points ◽  
Nearest Points

Given a closed set$C$in a Banach space$(X,\Vert \cdot \Vert )$, a point$x\in X$is said to have a nearest point in$C$if there exists$z\in C$such that$d_{C}(x)=\Vert x-z\Vert$, where$d_{C}$is the distance of$x$from$C$. We survey the problem of studying the size of the set of points in$X$which have nearest points in$C$. We then turn to the topic of delta convex functions and indicate how it is related to finding nearest points.

scholarly journals Order preserving and order reversing operators on the class of convex functions in Banach spaces

2015 ◽  
Vol 268 (1) ◽  
pp. 73-92 ◽  
Author(s):  
Alfredo N. Iusem ◽  
Daniel Reem ◽  
Benar F. Svaiter
Keyword(s):  
Banach Spaces ◽  
Convex Functions

scholarly journals Quotients of Continuous Convex Functions on Nonreflexive Banach Spaces

2007 ◽  
Vol 55 (3) ◽  
pp. 211-217 ◽  
Author(s):  
P. Holický ◽  
O. F. K. Kalenda ◽  
L. Veselý ◽  
L. Zajíček
Keyword(s):  
Banach Spaces ◽  
Convex Functions

scholarly journals Strongly Convex Functions of Higher Order Involving Bifunction

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1028 ◽  
Author(s):  
Bandar B. Mohsen ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
Mihai Postolache
Keyword(s):  
Banach Spaces ◽  
Convex Functions ◽  
Higher Order ◽  
Strongly Convex Functions ◽  
Strongly Convex ◽  
New Concepts ◽  
Special Cases ◽  
Novel Applications

Some new concepts of the higher order strongly convex functions involving an arbitrary bifuction are considered in this paper. Some properties of the higher order strongly convex functions are investigated under suitable conditions. Some important special cases are discussed. The parallelogram laws for Banach spaces are obtained as applications of higher order strongly affine convex functions as novel applications. Results obtained in this paper can be viewed as refinement and improvement of previously known results.

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