The famous Banach contraction principle (see, e.g., [1]) plays an important role in various fields of nonlinear analysis and applied mathematical analysis. Many authors investigated and established generalizations in various different directions of the Banach contraction principle in the past; see [1-22] and references therein. In 1969, Nadler [2] first proved a set-valued generalized version o...

This paper develops some aspects of stochastic calculus via regularization to Banach valued processes. An original concept of χ-quadratic variation is introduced, where χ is a subspace of the dual of a tensor product B ⊗ B where B is the values space of some process X process. Particular interest is devoted to the case when B is the space of real continuous functions defined on [−τ, 0], τ > 0. ...

Abstract We prove stronger variants of a multiplier theorem Kislyakov. The key ingredients are based on ideas Kislyakov and the Kahane–Salem–Zygmund inequality. As by-product, we show various theorems for spaces trigonometric polynomials n -dimensional torus $\mathbb {T}^n$ or Boolean cubes $\{-1,1\}^N$ . Our more abstract approach local Banach space theory has advantage that it allows to consi...

In this paper, we prove that the topological dual of the Banach space of bounded measurable functions with values in the space of nuclear operators, furnished with the natural topology, is isometrically isomorphic to the space of finitely additive linear operator-valued measures having bounded variation in a Banach space containing the space of bounded linear operators. This is then applied to ...

In this paper, we consider completely generalized nonlinear quasi-variational-like inclusions in Banach spaces and propose an Ishikawa type iterative algorithm for computing their approximate solutions by applying the new notion of Jη-proximal mapping given in [R. Ahmad, A.H. Siddiqi, Z. Khan, Proximal point algorithm for generalized multi-valued nonlinear quasi-variational-like inclusions in B...

We give an answer to the Problem 11.6 posed by Stephen Simons in his book ”From Hahn-Banach to Monotonicity”: Do there exist a nonzero finite dimensional Banach space and a pair of extended real-valued, proper and convex functions which is totally Fenchel unstable? The answer is negative.

We will consider the Banach space valued differential equation y′(t) = Ay(t) , where A is an n× n complex matrix. We give a necessary and sufficient condition in order that the equation have the Hyers-Ulam stability. As a Corollary, we prove that the Banach space valued linear differential equation with constant coefficients y(n)(t) + an−1y(n−1)(t) + · · ·+ a1y′(t) + a0y(t) = 0 has the Hyers-Ul...