Abstract
This paper deals with Cauchy problems and nonlocal problems for non-linear Stieltjes differential equations corresponding to a certain function g. We establish existence and uniqueness results for nonlinear equations with initial value or nonlocal conditions in the space ℬ𝒞 g ([0, H], ℝ) using fixed point methods and g-topology theory. We introduce the concepts of Ulam-Hyers (UH) and generalized Ulam-Hyers-Rassias (UHR) stability and present Ulam type stability results for linear and nonlinear equations in the spaces 𝒜𝒞 g ([0, H], ℝ) ⊂ ℬ𝒞 g ([0, H], ℝ) and ℬ𝒞 g ([0, H], ℝ). Finally, numerical examples are given to illustrate our results.
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