Related papers: Generalized variational inequalities for maximal m…
This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust stability properties of constrained set-valued mappings/multifunctions between…
We show that any bounded operator $T$ on a separable, reflexive, infinite-dimensional Banach space $X$ admits a rank one perturbation which has an invariant subspace of infinite dimension and codimension. In the non-reflexive spaces, we…
Some additive reverses of the generalised triangle inequality in normed linear spaces are given. Applications for complex numbers are provided as well.
Let $(X_i, \mathcal{F}_i)_{i\geq1}$ be a martingale difference sequence in a smooth Banach space. Let $S_n=\sum_{i=1}^nX_i, n\geq 1,$ be the partial sums of $(X_i, \mathcal{F}_i)_{i\geq 1}$. We give upper bounds on the quantity…
In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are…
For the class of systems of PDEs, for which infinitesimal translations (with respect to some (in)dependent variables) possess specific finite-dimensional invariant subspaces of the space of generalized symmetries of the system considered.…
In functional analysis it is of interest to study the following general question: Is the uniform version of a property that holds in all Banach spaces also valid in all Banach spaces? Examples of affirmative answers to the above question…
In this paper we lay the foundations for the Morse theoretical study of strongly indefinite functionals on Banach manifolds by developing the local theory for a specific model class that captures several key analytical features also arising…
In this work, an extension of the generalized mixed Schwarz inequality is proved. A companion of the generalized mixed Schwarz inequality is established by merging both Cartesian and Polar decompositions of operators. Based on that some…
Let $E$ be a uniformly smooth and uniformly convex real Banach space and $E^*$ be its dual space. Suppose $A : E\rightarrow E^*$ is bounded, strongly monotone and satisfies the range condition such that $A^{-1}(0)\neq \emptyset$. Inspired…
Motivated by the local theory of Banach spaces we introduce a notion of finite representability for metric spaces. This allows us to develop a new technique for comparing the generalized roundness of metric spaces. We illustrate this…
In the context of general Banach spaces characterizations for the maximal monotonicity of operators with non-empty domain interior as well as stronger continuity properties for such operators are provided.
We introduce a generalized forward-backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of…
Banach's fixed point theorem in linear n-normed space is being developed. Also, we present several theorems on fixed points in linear n-normed space.
In this paper, we introduce a new class of subsets of bounded linear operators between Banach spaces which is p-version of the uniformly completely continuous sets. Then, we study the relationship between these sets with the equicompact…
In this paper we focus on different -- global, semi-local and local -- versions of Hoffman type inequalities expressed in a variational form. In a first stage our analysis is developed for generic multifunctions between metric spaces and we…
The objective of this work is the construction of `Boyd-Wong fixed point theorem' in the setting of generalized parametric metric space and discussion its application on existence criteria of solutions to a second order initial value…
Solutions of a variational inequality are found by giving conditions for the monotone convergence with respect to a cone of the Picard iteration corresponding to its natural map. One of these conditions is the isotonicity of the projection…
In this paper we extend the coupled fixed point theorems for mixed monotone operators $F:X \times X \rightarrow X$ obtained in [T.G. Bhaskar, V. Lakshmikantham, \textit{Fixed point theorems in partially ordered metric spaces and…
We develop a semismooth Newton framework for the numerical solution of fixed-point equations that are posed in Banach spaces. The framework is motivated by applications in the field of obstacle-type quasi-variational inequalities and…