The stability of a connection on Hermitian vector bundles over a Riemannian manifold

2016 ◽  
Vol 09 (01) ◽  
pp. 1650001
Author(s):  
Rohollah Bakhshandeh-Chamazkoti ◽  
Mehdi Nadjafikhah
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Riemannian Manifold ◽  
Vector Bundles ◽  
Fixed Point Method ◽  
Point Method ◽  
The Stability ◽  
Rassias Stability ◽  
Hermitian Vector Bundles

In this attempt, the stability of a connection on Hermitian vector bundles over a Riemannian manifold for the generalized Jensen-type functional equation [Formula: see text] is discussed. In fact, the main purpose of this paper is to prove the generalized Hyers–Ulam–Rassias stability of connection on between Hermitian [Formula: see text] and [Formula: see text]. Also we will use the fixed point method to prove the stability of this connection for the above generalized Jensen-type functional equation.

scholarly journals On the Stability of an -Variables Functional Equation in Random Normed Spaces via Fixed Point Method

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
A. Ebadian ◽  
M. Eshaghi Gordji ◽  
H. Khodaei ◽  
R. Saadati ◽  
Gh. Sadeghi
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Method ◽  
Point Method ◽  
Integer Number ◽  
Normed Spaces ◽  
Random Normed Spaces ◽  
The Stability ◽  
Rassias Stability

At first we find the solution of the functional equation where is an integer number. Then, we obtain the generalized Hyers-Ulam-Rassias stability in random normed spaces via the fixed point method for the above functional equation.

A fixed point approach to the stability of sextic Lie *-derivations

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4933-4944
Author(s):  
Dongseung Kang ◽  
Heejeong Koh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Single Case ◽  
Fixed Point Method ◽  
Point Method ◽  
Fixed Point Approach ◽  
The Stability ◽  
The Given ◽  
Lie Derivations

We obtain a general solution of the sextic functional equation f (ax+by)+ f (ax-by)+ f (bx+ay)+ f (bx-ay) = (ab)2(a2 + b2)[f(x+y)+f(x-y)] + 2(a2-b2)(a4-b4)[f(x)+f(y)] and investigate the stability of sextic Lie *-derivations associated with the given functional equation via fixed point method. Also, we present a counterexample for a single case.

Ulam–Hyers stabilities of a generalized composite functional equation in non-Archimedean spaces

2016 ◽  
Vol 7 (4) ◽  
Author(s):  
Pasupathi Narasimman ◽  
John Michael Rassias
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Method ◽  
Point Method ◽  
Normed Spaces ◽  
Composite Functional Equation ◽  
Rassias Stability

AbstractIn this paper, we introduce a new generalized composite functional equation and prove its Hyers–Ulam–Rassias stability, Ulam–Găvruta–Rassias stability and Ulam–J. Rassias stability in non-Archimedean normed spaces using a fixed point method.

scholarly journals Fixed Points and the Stability of an AQCQ-Functional Equation in Non-Archimedean Normed Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Choonkil Park
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Quartic Functional Equation ◽  
The Stability

Using fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equationf(x+2y)+f(x−2y)=4f(x+y)+4f(x−y)−6f(x)+f(2y)+f(−2y)−4f(y)−4f(−y)in non-Archimedean Banach spaces.

scholarly journals The Stability of a Quadratic Functional Equation with the Fixed Point Alternative

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Choonkil Park ◽  
Ji-Hye Kim
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Method ◽  
Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
The Stability

Lee, An and Park introduced the quadratic functional equationf(2x+y)+f(2x−y)=8f(x)+2f(y)and proved the stability of the quadratic functional equation in the spirit of Hyers, Ulam and Th. M. Rassias. Using the fixed point method, we prove the generalized Hyers-Ulam stability of the quadratic functional equation in Banach spaces.

Sign in / Sign up

Export Citation Format

Share Document