Related papers: A general variational principle and some of its ap…

For an operator T from X to Y denote m(T) the infimum of $||Tx||$ on the unit sphere $S_X$ of X. A sequence $(x_n)$ in $S_X$ is said to be minimizing for T if $||Tx_n||$ tends to m(T). In 2020 U. S. Chakraborty introduced and studied the…

In this paper a new variational approach concerning functions (continuous) over Hilbert spaces is presented.

Let $X$ be a given Banach space and let $M$, $N$ be two orthogonal $X$-valued local martingales such that $N$ is weakly differentially subordinate to $M$. The paper contains the proof of the estimate $$ \mathbb E \Psi(N_t) \leq…

We investigate the existence of subinvariant metric functionals for commuting families of nonexpansive mappings in noncompact subsets of Banach spaces. Our findings underscore the practicality of metric functionals when searching for fixed…

In this paper, we show that several extension of Banach contraction principle, can be easily derived from the Caristi's theorem is one of the useful generalization of Banach contraction principle in the setting of the complete metric…

In this article we obtain some positive results about the existence of a common nontrivial invariant subspace for $N$-tuples of not necessarily commuting operators on Banach spaces with a Schauder basis. The concept of joint quasinilpotence…

Let f be local diffeomorphism between real Banach spaces. We prove that if the locally Lipschitz functional F(x)=1/2|f(x)-y|^2 satisfies the Chang Palais-Smale condition for all y in the target space of f, then f is a norm-coercive global…

In this paper, we study the differential inclusion associated to the minimal surface system for two-dimensional graphs in $\mathbb{R}^{2 + n}$. We prove regularity of $W^{1,2}$ solutions and a compactness result for approximate solutions of…

In the recent paper \cite{Aza:19} D Azagra studies the global shape of continuous convex functions defined on a Banach space $X$. More precisely, when $X$ is separable, it is shown that for every continuous convex function…

The center of interest in this work are variational problems with integral functionals depending on special nonlocal gradients. The latter correspond to truncated versions of the Riesz fractional gradient, as introduced in [Bellido, Cueto &…

We study Banach spaces X with a strongly asymptotic l_p basis (any disjointly supported finite set of vectors far enough out with respect to the basis behaves like l_p) which are minimal (X embeds into every infinite dimensional subspace).…

By using the Principle of Local Reflexivity (PLR), we prove that for every two Banach spaces $E$ and $X$ there exists a suitable ultrafilter $\mathcal{U}$ such that $ \mathcal{F}(E,X)^*,$ the dual space of the finite rank operators, can be…

We prove the existence of a weakly dependent strictly stationary solution of the equation $ X_t=F(X_{t-1},X_{t-2},X_{t-3},...;\xi_t)$ called {\em chain with infinite memory}. Here the {\em innovations} $\xi_t$ constitute an independent and…

In this paper, some existence results for sign-changing critical points of locally Lipschitz functionals in real Banach space are obtained by the method combining the invariant sets of descending ow method with a quantitative deformation.…

By methods of harmonic analysis, we identify large classes of Banach spaces invariant of periodic Fourier multipliers with symbols satisfying the classical Marcinkiewicz type conditions. Such classes include general (vector-valued) Banach…

Let $X$ be a real Banach space with a normalized duality mapping uniformly norm-to-weak$^\star$ continuous on bounded sets or a reflexive Banach space which admits a weakly continuous duality mapping $J_{\Phi}$ with gauge $\phi$. Let $f$ be…

The present paper is concerned with some representatons of linear mappings of continuous functions into locally convex vector spaces, namely: If X is a complete Hausdorff locally convex vector space, then a general form of weakly compact…

Let $X$ be a real locally uniformly convex Banach space and $X^*$ be the dual space of $X$. Let $\varphi:\mathbf R_+\to \mathbf R_+$ be a strictly increasing and continuous function such that $\varphi(0) = 0$, $\varphi(r) \to \infty$ as…

This appendix provides a short proof for sample path continuity of the Brownian motion induced by an arbitrary centered Gaussian measure on a separable Banach space, and also some perturbation results for the spectrum of compact…

In [8] probabilistic methods, in particular a variant of the Weak Law of Large Numbers related to the Bernoulli distribution, have been used to show that for every infinite compact spaces K and L there exists a sequence $(\mu_n)$ of…