Infinite discrete sets of limit points of iterative sequences of continuous functions

1981 ◽  
Vol 22 (1) ◽  
pp. 64-69
Author(s):  
R. Graw ◽  
M. Kuczma
Keyword(s):  
Continuous Functions ◽  
Limit Points

scholarly journals The Structure of Disjoint Groups of Continuous Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Hojjat Farzadfard ◽  
B. Khani Robati
Keyword(s):  
Piecewise Linear ◽  
General Structure ◽  
Open Interval ◽  
Continuous Functions ◽  
Cyclic Groups ◽  
The Third ◽  
Iteration Group ◽  
Limit Points ◽  
Special Case

LetIbe an open interval. We describe the general structure of groups of continuous self functions onIwhich are disjoint, that is, the graphs of any two distinct elements of them do not intersect. Initially the class of all disjoint groups of continuous functions is divided in three subclasses: cyclic groups, groups the limit points of their orbits are Cantor-like sets, and finally those the limit points of their orbits are the whole intervalI. We will show that (1) each group of the second type is conjugate, via a specific homeomorphism, to a piecewise linear group of the same type; (2) each group of the third type is a subgroup of a continuous disjoint iteration group. We conclude the Zdun's result on the structure of disjoint iteration groups of continuous functions as special case of our results.

Approximation in statistical sense to B -continuous functions by positive linear operators

2010 ◽  
Vol 47 (3) ◽  
pp. 289-298 ◽  
Author(s):  
Fadime Dirik ◽  
Oktay Duman ◽  
Kamil Demirci
Keyword(s):  
Compact Subset ◽  
Real Line ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Statistical Approximation ◽  
Classical Version ◽  
Statistical Sense

In the present work, using the concept of A -statistical convergence for double real sequences, we obtain a statistical approximation theorem for sequences of positive linear operators defined on the space of all real valued B -continuous functions on a compact subset of the real line. Furthermore, we display an application which shows that our new result is stronger than its classical version.

Almost Somewhat Near Continuity and Near Regularity

2021 ◽  
Vol 7 (1) ◽  
pp. 88-99
Author(s):  
Zanyar A. Ameen
Keyword(s):  
Continuous Function ◽  
Continuous Functions ◽  
One To One ◽  
Nearly Continuous

AbstractThe notions of almost somewhat near continuity of functions and near regularity of spaces are introduced. Some properties of almost somewhat nearly continuous functions and their connections are studied. At the end, it is shown that a one-to-one almost somewhat nearly continuous function f from a space X onto a space Y is somewhat nearly continuous if and only if the range of f is nearly regular.

Investigation of Limit Points and Separation Axioms Using Supra $\beta$-Open Sets

2020 ◽  
Vol 32 (2) ◽  
pp. 171-187
Author(s):  
T. M. Al-Shami ◽  
E. A. Abo-Tabl ◽  
B. A. Asaad
Keyword(s):  
Separation Axioms ◽  
Limit Points

On existence result of a class of nonlinear integral equation

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3593-3597
Author(s):  
Ravindra Bisht
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Existence Result ◽  
Nonlinear Integral Equation ◽  
Continuous Functions ◽  
Concave Functions ◽  
Real Numbers ◽  
Fixed Point Techniques ◽  
Uniqueness Of A Solution

Combining the approaches of functionals associated with h-concave functions and fixed point techniques, we study the existence and uniqueness of a solution for a class of nonlinear integral equation: x(t) = g1(t)-g2(t) + ? ?t,0 V1(t,s)h1(s,x(s))ds + ? ?T,0 V2(t,s)h2(s,x(s))ds; where C([0,T];R) denotes the space of all continuous functions on [0,T] equipped with the uniform metric and t?[0,T], ?,? are real numbers, g1, g2 ? C([0, T],R) and V1(t,s), V2(t,s), h1(t,s), h2(t,s) are continuous real-valued functions in [0,T]xR.

ON ε-CONTINUOUS FUNCTIONS

1995 ◽  
Vol 21 (1) ◽  
pp. 203
Author(s):  
Banaszewski
Keyword(s):  
Continuous Functions

ON THREADING CONTINUOUS FUNCTIONS THROUGH COMPACT SETS

1982 ◽  
Vol 8 (2) ◽  
pp. 455
Author(s):  
Akemann ◽  
Bruckner
Keyword(s):  
Continuous Functions ◽  
Compact Sets

I-density Continuous Functions

1989 ◽  
Vol 15 (1) ◽  
pp. 13
Author(s):  
Ciesielski ◽  
Larson ◽  
Ostaszewski
Keyword(s):  
Continuous Functions
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