In this paper, we introduce the Pettis integral of fuzzy mappings in Banach spaces using the Pettis integral of closed set-valued mappings. We investigate the relations between the Pettis integral, weak integral and integral of fuzzy mappings in Banach spaces and obtain some properties of the Pettis integral of fuzzy mappings in Banach spaces.

A Banach spaceX with the property that every absolutely continuousX−valued function is almost everywhere differentiable is said to be a Radon-Nikodym space [7, pp. 217–219] or [2, 13] (see also [3]). For example, every reflexive Banach space (in particular, every Hilbert space) is a Radon-Nikodym space, but the space L∞ [0, 1] of all K−valued, essentially bounded functions defined on the interv...

In this paper we give a simple proof of inequalities of integrals of functions which are the composition of nonnegative continous convex functions on a vector space R and vector-valued functions in a weakly compact subset of a Banach vector space generated by m Lμ-spaces for 1 ≤ p < +∞. Also, the same inequalities hold if these vector-valued functions are in a weakly* compact subset of a Banach...

We give a comparison inequality that allows one to estimate the tail probabilities of sums of independent Banach space valued random variables in terms of those of independent identically distributed random variables. More precisely, let X1, . . . , Xn be independent Banach-valued random variables. Let I be a random variable independent of X1, . . . , Xn and uniformly distributed over {1, . . ....

In this paper the multi-valued versions of some well-known hybrid fixed point theorems of Dhage [6, 7] in Banach algebras are proved. As an application, an existence theorem for a certain integral inclusion in Banach algebras is proved.

In recent years, Fourier multiplier theorems in vector–valued function spaces have found many applications in embedding theorems of abstract function spaces and in theory of differential operator equations, especially in maximal regularity of parabolic and elliptic differential–operator equations. Operator–valued multiplier theorems in Banach–valued function spaces have been discussed extensive...

If X is a Banach space then the Banach space c(X) of all X-valued convergent sequences contains a nonvoid bounded closed convex body V such that no point in C(X) \ V has a nearest point in V .

Contents 1. Introduction 963 2. A game called í µí±ƒ-orderings 967 2.1. On í µí±Ÿ-removed í µí±ƒ-orderings 968 2.2. On í µí±ƒ-orderings of order ℎ 969 3. Rings of integer-valued polynomials 969 3.1. Polynomials with integer-valued divided differences 970 3.2. Integer-valued polynomials having a given modulus 973 4. Smooth functions on compact subsets of local fields 976 4.1. The Banach space of...

We show that the centraliser of the space of n-fold symmetric injective tensors, n ≥ 2, on a real Banach space is trivial. With a geometric condition on the set of extreme points of its dual, the space of integral polynomials we obtain the same result for complex Banach spaces. We give some applications of this results to centralisers of spaces of homogeneous polynomials and complex Banach spac...