Open access

DOI: 10.24193/fpt-ro.2017.2.59

Authors: Marcel-Adrian Șerban

Abstract: For a triangular operator A:X x Y → X x Y, A=(B,C), where B:X → X and C:X x Y → Y we study in which conditions on operators B:X → X and C:X x Y → Y we have that:

1. the fixed point problem for triangular operator A=(B,C) is well posed
2. the operator A=(B,C) has the Ostrowski property
3. the fixed point equation (x,y)=A(x,y) is generalized Ulam-Hyers stable

Key Words and Phrases: Cauchy lemma, fixed point, fibre contraction principle, well-posedness of the fixed point problem, Ostrowski property, Ulam-Hyers stability, generalized Ulam-Hyers stability.

2010 Mathematics Subject Classification: 47H10, 54H25, 65J15, 34A34, 34A12, 45G10.

Published on-line: June 1st, 2017.

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