In this paper, we prove the existence of continuous solutions of a Volterra integral inclusion involving the Henstock-Kurzweil-Pettis integral. Since this kind of integral is more general than the Bochner, Pettis and Henstock integrals, our result extends many of the results previously obtained in the single-valued setting or in the set-valued case.

A copula-based method to integrate a real vector-valued function, obtaining a single real number, is discussed. Special attention is paid to the case when the underlying universe is finite. The integral considered here is shown to be an extension of [0, 1]-valued copula-based universal integrals.

The semigroup-valued integral of M. Sion [S] is reformulated for a general notion of approximation by sums of values taken by a set function integrand. A convergence in measure theorem is established, which yields both his pointwise dominated convergence theorem as well as an integrability criterion which specializes to his existence theorem. In [S] M. Sion introduced and developed an "integral...

Abstract In this work, we introduce the notions about Riemann-Liouville fractional integrals for interval-valued functions on co-ordinates. We also establish Hermite-Hadamard and some related inequalities co-ordinated convex by applying newly defined integrals. The results of present paper are extension several previously published results.

By using the concepts of fuzzy number fuzzy measures and fuzzy valued functions a theory of fuzzy integrals is investigated. In this paper we have established the fuzzy version of Generalised monotone Convergence theorem and generalised Fatous lemma. 1. Introduction In the preceding paper [2], it is introduced that a concept of fuzzy number fuzzy measures, defined the fuzzy integral of a functi...

Using fractional calculus we define integrals of the form ∫ b a f(xt)dyt, where x and y are vector-valued Hölder continuous functions of order β ∈ ( 1 3 , 1 2 ) and f is a continuously differentiable function such that f ′ is λ-Höldr continuous for some λ > 1 β − 2. Under some further smooth conditions on f the integral is a continuous functional of x, y, and the tensor product x ⊗ y with respe...

In this paper, we shall firstly illustrate why we should discuss the Aumann type set-valued Lebesgue integral of a set-valued stochastic process with respect to time t under the condition that the set-valued stochastic process takes nonempty compact subset of d-dimensional Euclidean space. After recalling some basic results about set-valued stochastic processes, we shall secondly prove that the...

We consider a real-valued path; it is possible to associate a tree to this path, and we explore the relations between the tree, the properties of p-variation of the path, and integration with respect to the path. In particular, the fractal dimension of the tree is estimated from the variations of the path, and Young integrals with respect to the path, as well as integrals from the rough paths t...