Iterative roots of continuous functions and Hyers–Ulam stability

2020 ◽  
Author(s):  
Veerapazham Murugan ◽  
Rajendran Palanivel
Keyword(s):  
Continuous Functions ◽  
Ulam Stability ◽  
Iterative Roots

On Hyers–Ulam Stability of Cauchy and Wilson Equations

2004 ◽  
Vol 11 (1) ◽  
pp. 69-82
Author(s):  
Elhoucien Elqorachi ◽  
Mohamed Akkouchi
Keyword(s):  
Topological Group ◽  
Compact Support ◽  
Stability Problem ◽  
Functional Equations ◽  
Identity Element ◽  
Continuous Functions ◽  
Dirac Measure ◽  
Ulam Stability ◽  
Natural Extensions ◽  
Ulam Stability Problem

Abstract We study the Hyers–Ulam stability problem for the Cauchy and Wilson integral equations where 𝐺 is a topological group, 𝑓, 𝑔 : 𝐺 → ℂ are continuous functions, μ is a complex measure with compact support and σ is a continuous involution of 𝐺. The result obtained in this paper are natural extensions of the previous works concerning the Hyers–Ulam stability of the Cauchy and Wilson functional equations done in the particular case of μ=δe : The Dirac measure concentrated at the identity element of 𝐺.

scholarly journals On the Hyers-Ulam Stability of First-Order Impulsive Delay Differential Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Akbar Zada ◽  
Shah Faisal ◽  
Yongjin Li
Keyword(s):  
Continuous Functions ◽  
Gronwall Lemma ◽  
Ulam Stability ◽  
Order Ordinary Differential Equation ◽  
First Order ◽  
Impulsive Delay Differential Equations ◽  
Impulsive Delay ◽  
Delay Differential ◽  
Rassias Stability ◽  
Single Constant

This paper proves the Hyers-Ulam stability and the Hyers-Ulam-Rassias stability of nonlinear first-order ordinary differential equation with single constant delay and finite impulses on a compact interval. Our approach uses abstract Gronwall lemma together with integral inequality of Gronwall type for piecewise continuous functions.

Iterative roots of continuous functions with non-isolated forts

2017 ◽  
Vol 28 (1) ◽  
pp. 89-93
Author(s):  
V. Murugan ◽  
M. Suresh Kumar
Keyword(s):  
Continuous Functions ◽  
Iterative Roots

scholarly journals Subcommuting and comparable iterative roots of order preserving homeomorphisms

2019 ◽  
Vol 26 (1/2) ◽  
pp. 203-210
Author(s):  
Veerapazham Murugan ◽  
Murugan Suresh Kumar
Keyword(s):  
Continuous Functions ◽  
Iterative Roots ◽  
Points Of Coincidence ◽  
Set Of Points

It is known that the iterative roots of continuous functions are not necessarily unique, if it exist. In this note, by introducing the set of points of coincidence, we study the iterative roots of order preserving homeomorphisms. In particular, we prove a characterization of identical iterative roots of an order preserving homeomorphism using the points of coincidence of functions.

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.

On the stability of a nonic functional equation in quasi-normed spaces

2016 ◽  
Vol 12 (3) ◽  
pp. 4368-4374
Author(s):  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Normed Spaces ◽  
The Stability

In this paper, we extend normed spaces to quasi-normed spaces and prove the generalized Hyers-Ulam stability of a nonic functional equation:$$\aligned&f(x+5y) - 9f(x+4y) + 36f(x+3y) - 84f(x+2y) + 126f(x+y) - 126f(x)\\&\qquad + 84f(x-y)-36f(x-2y)+9f(x-3y)-f(x-4y) = 9 ! f(y),\endaligned$$where $9 ! = 362880$ in quasi-normed spaces.

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.

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.

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