J. Fixed Point Theory Appl. (2019) 21:73 https://doi.org/10.1007/s11784-019-0711-1 c  Springer Nature Switzerland AG 2019 Journal of Fixed Point Theory and Applications Existence and stability results for a system of operator equations via ﬁxed point theory for nonself orbital contractions Adrian Petru¸ sel, Gabriela Petru¸ sel and Jen-Chih Yao Abstract. In this paper, we will present existence, stability, and local- ization results for a general system of operator equations in complete metric spaces. The approach is based on the application of some ﬁxed point theorems for orbital contractions in complete metric space. In particular, the coupled ﬁxed point problem is considered. Mathematics Subject Classiﬁcation. 47H10, 54H25. Keywords. Single-valued operator, ﬁxed point, orbital contraction, cou- pled ﬁxed point, data dependence, well-posedness, Ulam–Hyers stability, Ostrowski property, ordered metric space, application. 1. Introduction The most useful ﬁxed point theorem in the metric context is the Contraction Principle (CP) proved in 1922 by Stefan Banach for self contractions on Banach spaces. This principle was later extended, by Renato Caccioppoli, to self contractions on complete metric spaces. An important extension of the (CP) is the case when the contraction condition is assumed only for pairs (x, y) from the graph of the operator. Another research direction in ﬁxed point theory is related to the case of nonself operators (see [1, 15, 16, 19–21], and so on). The case of nonself operators from a (closed or open) ball to the whole space has been extensively studied (see [8, 14], etc.). On the other hand, the notion of coupled ﬁxed point is very useful in the study of operator equation systems. The topic gets a fast development after the publication of the inﬂuential papers of Guo and Lakshmikantham [6], Gnana Bhaskar and Lakshmikantham [4], Lakshmikantham and ´ Ciri´ c [7], and Berinde [2] (see also [5, 11, 12] for various applications). The results were extended to various spaces and some other related problems, such as coupled coincidence problems, tripled ﬁxed point problems, multiple ﬁxed point problems, and so on. 0123456789().: V,-vol