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Porous sets for mutually nearest points in Banach spaces

100%

Li C. , Myjak J.

Opuscula Mathematica

2008

tom Vol. 28, no. 1

73-82

Let B(X) denote the family of all nonempty closed bounded subsets of a real Banach space X, endowed with the Hausdorff metric. For E, F ∈ B (X) we set [formula]. Let D denote the closure (under the maximum distance) of the set of all (E, F) ∈ B (X) x B (X) such that λE,F > 0. It is proved that the set of all (E, F) ∈ D for which the minimization problem [formula] fails to be well posed in a σ-porous subset of D.

Introducing and solving the hesitant fuzzy system AX = B

88%

Babakordi F. , Allahviranloo T.

Control and Cybernetics

2021

tom Vol. 50, No. 4

553--574

In this paper the solution for hesitant fuzzy system as AX = B is introduced where A is an n×n known hesitant fuzzy matrix, B is an n×1 known hesitant fuzzy vector and X is an n×1 unknown hesitant fuzzy vector. First, L∞-norm and L1-norm of a hesitant fuzzy vector are introduced. Then, the concepts of hesitant fuzzy zero, ’almost equal’ and ’less than’ and ’equal’ are defined for two hesitant fuzzy numbers. Finally, using a minimization problem; the hesitant fuzzy system is solved. At the end, some numerical examples are presented to show the effectiveness of the proposed method.

On the proximal point algorithm and demimetric mappings in CAT(0) spaces

63%

Aremu K. O. , Izuchukwu C. , Ugwunnadi G. C. , Mewomo O. T.

Demonstratio Mathematica

2018

tom Vol. 51, nr 1

277--294

In this paper, we introduce and study the class of demimetric mappings in CAT(0) spaces. We then propose a modified proximal point algorithm for approximating a common solution of a finite family of minimization problems and fixed point problems in CAT(0) spaces. Furthermore, we establish strong convergence of the proposed algorithm to a common solution of a finite family of minimization problems and fixed point problems for a finite family of demimetric mappings in complete CAT(0) spaces. A numerical example which illustrates the applicability of our proposed algorithm is also given. Our results improve and extend some recent results in the literature.

Stability of solutions for a class of convex minimization problems on reflective Banach spaces

51%

Zaslavski A. J.

Journal of Mathematics and Applications

2008

tom Vol. 30

151-160

In this paper we study stability of solutions of minimization problems �(x) → min, x ∈ C, where � is a convex lower semicontinuous function and a set C is the countable intersection of a decreasing sequence of closed sets Ci in a reflexive Banach space X.