Displaying similar documents to “New extension of the variational McShane integral of vector-valued functions”

A penalty approach for a box constrained variational inequality problem

Zahira Kebaili, Djamel Benterki (2018)

Applications of Mathematics

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We propose a penalty approach for a box constrained variational inequality problem ( BVIP ) . This problem is replaced by a sequence of nonlinear equations containing a penalty term. We show that if the penalty parameter tends to infinity, the solution of this sequence converges to that of BVIP when the function F involved is continuous and strongly monotone and the box C contains the origin. We develop the algorithmic aspect with theoretical arguments properly established. The numerical results...

Some remarks on descriptive characterizations of the strong McShane integral

Sokol Bush Kaliaj (2019)

Mathematica Bohemica

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We present the full descriptive characterizations of the strong McShane integral (or the variational McShane integral) of a Banach space valued function f : W X defined on a non-degenerate closed subinterval W of m in terms of strong absolute continuity or, equivalently, in terms of McShane variational measure V F generated by the primitive F : W X of f , where W is the family of all closed non-degenerate subintervals of W .

Relations between multidimensional interval-valued variational problems and variational inequalities

Anurag Jayswal, Ayushi Baranwal (2022)

Kybernetika

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In this paper, we introduce a new class of variational inequality with its weak and split forms to obtain an L U -optimal solution to the multi-dimensional interval-valued variational problem, which is a wider class of interval-valued programming problem in operations research. Using the concept of (strict) L U -convexity over the involved interval-valued functionals, we establish equivalence relationships between the solutions of variational inequalities and the (strong) L U -optimal solutions...

Variational Henstock integrability of Banach space valued functions

Luisa Di Piazza, Valeria Marraffa, Kazimierz Musiał (2016)

Mathematica Bohemica

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We study the integrability of Banach space valued strongly measurable functions defined on [ 0 , 1 ] . In the case of functions f given by n = 1 x n χ E n , where x n are points of a Banach space and the sets E n are Lebesgue measurable and pairwise disjoint subsets of [ 0 , 1 ] , there are well known characterizations for Bochner and Pettis integrability of f . The function f is Bochner integrable if and only if the series n = 1 x n | E n | is absolutely convergent. Unconditional convergence of the series is equivalent to Pettis integrability...

Duality for a fractional variational formulation using η -approximated method

Sony Khatri, Ashish Kumar Prasad (2023)

Kybernetika

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The present article explores the way η -approximated method is applied to substantiate duality results for the fractional variational problems under invexity. η -approximated dual pair is engineered and a careful study of the original dual pair has been done to establish the duality results for original problems. Moreover, an appropriate example is constructed based on which we can validate the established dual statements. The paper includes several recent results as special cases. ...

Pressure and recurrence

Véronique Maume-Deschamps, Bernard Schmitt, Mariusz Urbański, Anna Zdunik (2003)

Fundamenta Mathematicae

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We deal with a subshift of finite type and an equilibrium state μ for a Hölder continuous function. Let αⁿ be the partition into cylinders of length n. We compute (in particular we show the existence of the limit) l i m n n - 1 l o g j = 0 τ ( x ) μ ( α ( T j ( x ) ) ) , where α ( T j ( x ) ) is the element of the partition containing T j ( x ) and τₙ(x) is the return time of the trajectory of x to the cylinder αⁿ(x).

Analytic semigroups generated on a functional extrapolation space by variational elliptic equations

Vincenzo Vespri (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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We prove that any elliptic operator of second order in variational form is the infinitesimal generator of an analytic semigroup in the functional space C - 1 , α ( Ω ) consinsting of all derivatives of hölder-continuous functions in Ω where Ω is a domain in n not necessarily bounded. We characterize, moreover the domain of the operator and the interpolation spaces between this and the space C - 1 , α ( Ω ) . We prove also that the spaces C - 1 , α ( Ω ) can be considered as extrapolation spaces relative to suitable non-variational...

Local analysis of a cubically convergent method for variational inclusions

Steeve Burnet, Alain Pietrus (2011)

Applicationes Mathematicae

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This paper deals with variational inclusions of the form 0 ∈ φ(x) + F(x) where φ is a single-valued function admitting a second order Fréchet derivative and F is a set-valued map from q to the closed subsets of q . When a solution z̅ of the previous inclusion satisfies some semistability properties, we obtain local superquadratic or cubic convergent sequences.

Finite element variational crimes in the case of semiregular elements

Alexander Ženíšek (1996)

Applications of Mathematics

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The finite element method for a strongly elliptic mixed boundary value problem is analyzed in the domain Ω whose boundary Ω is formed by two circles Γ 1 , Γ 2 with the same center S 0 and radii R 1 , R 2 = R 1 + ϱ , where ϱ R 1 . On one circle the homogeneous Dirichlet boundary condition and on the other one the nonhomogeneous Neumann boundary condition are prescribed. Both possibilities for u = 0 are considered. The standard finite elements satisfying the minimum angle condition are in this case inconvenient; thus...

A regularity theory for scalar local minimizers of splitting-type variational integrals

Michael Bildhauer, Martin Fuchs, Xiao Zhong (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Starting from Giaquinta’s counterexample [12] we introduce the class of splitting functionals being of ( p , q ) -growth with exponents p q < and show for the scalar case that locally bounded local minimizers are of class C 1 , μ . Note that to our knowledge the only C 1 , μ -results without imposing a relation between p and q concern the case of two independent variables as it is outlined in Marcellini’s paper [15], Theorem A, and later on in the work of Fusco and Sbordone [10], Theorem 4.2.