Best approximation theorems for almost cyclic contractions

2021 ◽  
Vol 23 (2) ◽  
Author(s):  
S. Sadiq Basha
Keyword(s):  
Best Approximation ◽  
Approximation Theorems ◽  
Cyclic Contractions

scholarly journals Some KKM theorems in modular function spaces

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1307-1313
Author(s):  
Nasrin Karamikabir ◽  
Abdolrahman Razani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Best Approximation ◽  
Modular Function ◽  
Function Spaces ◽  
Minimax Inequality ◽  
Approximation Theorems ◽  
Coincidence Theorem ◽  
Modular Function Spaces ◽  
Ky Fan

In this paper, a coincidence theorem is obtained which is generalization of Ky Fan?s fixed point theorem in modular function spaces. A modular version of Fan?s minimax inequality is proved. Moreover, some best approximation theorems are presented for multi-valued mappings.

NOTE ON JACKSON AND BERNSTE N TYPE APPROXIMATION THEOREMS IN THE CASE OF APPROXIMATION BY ALGEBRAIC POLYNOMIALS N THE SPACES L AND C

2000 ◽  
Vol 36 (3-4) ◽  
pp. 353-358 ◽  
Author(s):  
S. Pawelke
Keyword(s):  
Periodic Function ◽  
Best Approximation ◽  
Trigonometric Polynomials ◽  
Algebraic Polynomials ◽  
Cient Condition ◽  
Approximation Theorems ◽  
Type Approximation ◽  
The Best Approximation ◽  
Approximation By Algebraic Polynomials

We con ider the best approximation E (n,f)by algebraic polynomials of degree at most n for function f in L 1 (-1, 1)or C [-1, 1]and give imple necessary and u .cient condition for E (n,f)=O (n-.),n ›.,u ing the well-known results in the ca e of ap- proximation of periodic function by trigonometric polynomials.

scholarly journals A global optimality result using Geraghty type contraction

2014 ◽  
Vol 4 (2) ◽  
pp. 99-104 ◽  
Author(s):  
Binayak S. Choudhury ◽  
Pranati Maity ◽  
P. Konar
Keyword(s):  
Fixed Point ◽  
Best Approximation ◽  
Approximate Solutions ◽  
Global Optimality ◽  
Approximation Theorems ◽  
The Best Approximation ◽  
Optimal Values ◽  
Type Contraction

In this paper we prove two proximity point results for finding the distance between two sets. Unlike the best approximation theorems they provide with globally optimal values. Here our approach is to reduce the problem to that of finding optimal approximate solutions of some fixed point equations. We use Geraghty type contractive inequalities in our theorem. Two illustrative examples are given.

Some best-approximation theorems in tensor-product spaces

1981 ◽  
Vol 89 (3) ◽  
pp. 385-390 ◽  
Author(s):  
W. A. Light ◽  
E. W. Cheney
Keyword(s):  
Tensor Product ◽  
Best Approximation ◽  
Product Form ◽  
Product Spaces ◽  
Approximation Theorems ◽  
Univariate Functions ◽  
Bivariate Function ◽  
Image Position

We begin by describing a concrete example from the class of problems to be considered. A continuous bivariate function f defined on the square |t| ≤ 1, |s| ≤ 1 is to be approximated by a tensor-product form involving univariate functions. For example, the approximation may be prescribed to have the formin which the Ti are the Tchebycheff polynomials, and the coefficient functions xi(t) and yi(s) are to be chosen to achieve a good or best approximation. Will a best approximation exist? If so, how can it be obtained?

scholarly journals Best approximation theorems for composites of upper semicontinuous maps

1995 ◽  
Vol 51 (2) ◽  
pp. 263-272 ◽  
Author(s):  
Sehie Park
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Best Approximation ◽  
Broad Class ◽  
Compact Convex ◽  
Approximation Theorems ◽  
Upper Semicontinuous ◽  
Hausdorff Topological Vector Space ◽  
Locally Convex ◽  
Convex Subsets

Let (E, τ) be a Hausdorff topological vector space and (X, ω) a weakly compact convex subset of E with the relative weak topology ω. Recently, there have appeared best approximation and fixed point theorems for convex-valued upper semicontinuous maps F: (X, ω) → 2(E, τ) whenever (E, τ) is locally convex. In this paper, these results are extended to a very broad class of multifunctions containing composites of acyclic maps in a topological vector space having sufficiently many linear functionals. Moreover, we also obtain best approximation theorems for classes of multifunctions defined on approximatively compact convex subsets of locally convex Hausdorff topological vector spaces or closed convex subsets of Banach spaces with the Oshman property.

scholarly journals The Best Approximation Theorems and Fixed Point Theorems for Discontinuous Increasing Mappings in Banach Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Dezhou Kong ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Projection Operator ◽  
Best Approximation ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Generalized Projection ◽  
Approximation Theorems ◽  
Generalized Projection Operator

We prove that Fan’s theorem is true for discontinuous increasing mappingsfin a real partially ordered reflexive, strictly convex, and smooth Banach spaceX. The main tools of analysis are the variational characterizations of the generalized projection operator and order-theoretic fixed point theory. Moreover, we get some properties of the generalized projection operator in Banach spaces. As applications of our best approximation theorems, the fixed point theorems for non-self-maps are established and proved under some conditions. Our results are generalizations and improvements of the recent results obtained by many authors.

Sign in / Sign up

Export Citation Format

Share Document