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Abstract In this paper, we prove the Hyers-Ulam stability and the Hyers-Ulam-Rassias stability of a class of higher order nonlinear delay differential equations with multiple bounded variable delays on a compact interval. Result of existence and uniqueness of solution is obtained by fixed point approach. Meanwhile, for the first time, integral inequality of Grönwall-Bellman-Bihari's type with delay is applied to prove the stability theorem which made our results more generalized and interesting. [ABSTRACT FROM AUTHOR]

The purpose of this work is to fill a gap in the article Priya and Uthayakumar (2022) [13]. To prove fractals (fixed points), the authors of that article tried to connect two independent conceptual domains. This results in their main theorem being wrong and becoming a conjecture. This paper scrutinizes and presents both the concepts above to demonstrate fractals in the settings posed in that article. Using a proper definition, the correct theorem to achieve the purpose of that article is discussed. [ABSTRACT FROM AUTHOR]

Abstract: Let be a metric space endowed with a graph such that the set of vertices of coincides with . We define the notion of -Reich type maps and obtain a fixed point theorem for such mappings. This extends and subsumes many recent results which were obtained for other contractive type mappings on ordered metric spaces and for cyclic operators. [Copyright &y& Elsevier]

Abstract: We introduce a class of double-complex integral linear operators. Some geometric properties are investigated and a statistical approximation theorem is obtained. In a particular case, our operators turn into the complex Picard operators. [Copyright &y& Elsevier]

Abstract: Following [W.A. Kirk, P.S. Srinivasan, P. Veeramany, Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory 4 (1) (2003) 79–89], we present a fixed point theorem for cyclic -contractions and following [I.A. Rus, The theory of a metrical fixed point theorem: Theoretical and applicative relevances, Fixed Point Theory 9 (2) (2008) 541–559] we construct a theory of this fixed point theorem. This theory is in connection with data dependence, well-posedness of the fixed point problem, limit shadowing property and sequences of operators and fixed points. A Maia type fixed point theorem for cyclic -contractions is also given. [Copyright &y& Elsevier]