A generalization of Halpern’s iteration is investigated on a compact convex subset of a smooth Banach space. The modified iteration process consists of a combination of a viscosity term, an external sequence, and a continuous nondecreasing function of a distance of points of an external sequence, which is not necessarily related to the solution of Halpern’s iteration, a contractive mapping, and...

Let f (z1, . . . ,zk)∈ C(Ik,I) be a given function, where I is (bounded or unbounded) subinterval of R, and k ∈ N. Assume that f (y1, y2, . . . , yk) ≥ f (y2, . . . , yk, y1) if y1 ≥ max{y2, . . . , yk}, f (y1, y2, . . . , yk) ≤ f (y2, . . . , yk, y1) if y1 ≤ min{y2, . . . , yk}, and f is nondecreasing in the last variable zk. We then prove that every bounded solution of an autonomous differenc...

In this paper we study path-by-path uniqueness for multidimensional stochastic differential equations driven by the Brownian sheet. We assume that drift coefficient is unbounded, verifies a spatial linear growth condition and componentwise nondeacreasing. Our approach consists of showing result bounded nondecreasing using both local time-space representation law iterated logarithm sheets. The d...

In this article, we verify the existence and uniqueness of a positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form Dα 0+ x(t) + f(t, x(t)) = 0, 0 < t < 1, 2 < α ≤ 3, x(0) = x′(0) = 0, x′(1) = βx(ξ), where Dα 0+ denotes the standard Riemann-Liouville fractional derivative, 0 < ξ < 1 and 0 < β ξ < α− 1. Our analysis relies on the ...

In this paper, we study some existence and uniqueness results for systems of differential equations in which each the system involves a different Stieltjes derivative. Specifically, show that problems can only have one solution under Osgood condition, or even, Montel–Tonelli condition. We also explore guaranteeing these conditions. Along way, obtain interesting properties Lebesgue–Stieltjes int...

We show that the emptiness problem for two-way nondeterministic finite automata augmented with one reversal-bounded counter (i.e., the counter alternates between nondecreasing and nonincreasing modes a fixed number of times) operating on bounded languages (i.e., subsets of for some nonnull words ) is decidable, resolving a problem left open in [4,7]. The proof is a rather involved reduction to ...