In this paper, we study the existence of solutions of some nonlinear Volterra integral equations by using the techniques of measures of noncompactness and the Petryshyn's fixed point theorem in Banach space. We also present some examples of the integral equation to confirm the efficiency of our results.

In this paper, we generalize Fuzzy Banach contraction theorem establishedby V. Gregori and A. Sapena [Fuzzy Sets and Systems 125 (2002) 245-252]using notion of altering distance which was initiated by Khan et al. [Bull. Austral.Math. Soc., 30(1984), 1-9] in metric spaces.

In this paper, we first present the new concept of $2$-normed algebra. We investigate the structure of this algebra and give some examples. Then we apply a fixed point theorem to prove the stability and hyperstability of $(alpha, beta, gamma)$-derivations in $2$-Banach algebras.

In this paper, we investigate a new type of random $F$-contraction and obtain a common random fixed point theorem for a pair of self stochastic mappings in a separable Banach space. The existence of a unique solution for nonlinear fractional random differential equation is proved under suitable conditions.

A generalization of Phelps’ lemma to locally convex spaces is proven, applying its well-known Banach space version. We show the equivalence of this theorem, Ekeland’s principle and Danes̆’ drop theorem in locally convex spaces to their Banach space counterparts and to a Pareto efficiency theorem due to Isac. This solves a problem, concerning the drop theorem, proposed by G. Isac in 1997. We show...

Several generalizations of the Hahn–Banach extension theorem to K-convex multifunctions were stated recently in the literature. In this note we provide an easy direct proof for the multifunction version of the Hahn–Banach–Kantorovich theorem and show that in a quite general situation it can be obtained from existing results. Then we derive the Yang extension theorem using a similar proof as wel...

where Id is the identity operator on C[0, 1]. This equation is now called Daugavet equation. The Banach space X is said to have the Daugavet property when all compact operators on X satisfy the Daugavet equation. More information about the Daugavet spaces can be found in [Werner, 2001]. In the same paper was also posed the question, whether the Banach space of Lipschitz functions on unit square...

In this paper, we present a new concept of random contraction and prove a coupled random fixed point theorem under this condition which generalizes stochastic Banach contraction principle. Finally, we apply our contraction to obtain a solution of random nonlinear integral equations and we present a numerical example.

Cylindrical Wiener processes in real separable Banach spaces are defined, and an approximation theorem involving scalar Wiener processes is given for such processes. A weak stochastic integral for Banach spaces involving a cylindrical Wiener process as integrator and an operator-valued stochastic process as integrand is defined. Basic properties of this integral are stated and proved. A class o...