HYERS-ULAM STABILITY OF FIRST ORDER LINEAR DIFFERENCE OPERATORS ON BANACH SPACE

Arun Kumar Tripathy,Pragnya Senapati

doi:10.24297/jam.v14i1.7062

Abstract

In this work, the Hyers-Ulam stability of first order linear difference operator TP defined by (Tpu)(n) = âˆ†u(n) - p(n)u(n); is studied on the Banach space X = lâˆž, where p(n) is a sequence of reals.

Highlights

Let X = l∞ be the Banach space of all real valued functions u(n) defined for n ≥ 0
The general solution of Tp = v is of the form u(n) = (1 + p(i)) x0 + v(s) (1 + p(i))
DEFINITION 1.1 We say that the difference operator Tp has the Hyers-Ulam stability, if there exists a constant K ≥ 0 with the property: For every ≥ 0 and u, v ∈ D(I, X) satisfying Tpu−v ∞ ≤ there exists u0 ∈ D(I, X) such that Tpu0 = v and u−uo ∞ ≤ K

Summary

Introduction

The Hyers-Ulam stability of first order linear difference operator Tp defined by (Tpu)(n) = u(n) − p(n)u(n), is studied on the Banach space X = l∞, where p(n) is a sequence of reals. DEFINITION 1.1 We say that the difference operator Tp has the Hyers-Ulam stability, if there exists a constant K ≥ 0 with the property: For every ≥ 0 and u, v ∈ D(I, X) satisfying Tpu−v ∞ ≤ there exists u0 ∈ D(I, X) such that Tpu0 = v and u−uo ∞ ≤ K .

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Results

Conclusion