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Best approximation for nonconvex set in q -normed space

Hemant Kumar Nashine (2006)

Archivum Mathematicum

Some existence results on best approximation are proved without starshaped subset and affine mapping in the set up of q -normed space. First, we consider the closed subset and then weakly compact subsets for said purpose. Our results improve the result of Mukherjee and Som (Mukherjee, R. N., Som, T., A note on an application of a fixed point theorem in approximation theory, Indian J. Pure Appl. Math. 16(3) (1985), 243–244.) and Jungck and Sessa (Jungck, G., Sessa, S., Fixed point theorems in best...

Best approximation of coincidence points in metric trees

Bożena Piątek (2008)

Annales UMCS, Mathematica

In this work we present results on fixed points, pairs of coincidence points and best approximation for ε-semicontinuous mappings in metric trees. It is a generalization of the similar properties of upper and almost lower semicontinuous mappings.

Best approximations, fixed points and parametric projections

Tiziana Cardinali (2002)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

If f is a continuous seminorm, we prove two f-best approximation theorems for functions Φ not necessarily continuous as a consequence of our version of Glebov's fixed point theorem. Moreover, we obtain another fixed point theorem that improves a recent result of [4]. In the last section, we study continuity-type properties of set valued parametric projections and our results improve recent theorems due to Mabizela [11].

Best proximity point for proximal Berinde nonexpansive mappings on starshaped sets

Nuttawut Bunlue, Suthep Suantai (2018)

Archivum Mathematicum

In this paper, we introduce the new concept of proximal mapping, namely proximal weak contractions and proximal Berinde nonexpansive mappings. We prove the existence of best proximity points for proximal weak contractions in metric spaces, and for proximal Berinde nonexpansive mappings on starshape sets in Banach spaces. Examples supporting our main results are also given. Our main results extend and generalize some of well-known best proximity point theorems of proximal nonexpansive mappings in...

Boundary value problems for first order multivalued differential systems

Abdelkader Boucherif, N.Chiboub-Fellah Merabet (2005)

Archivum Mathematicum

We present some existence results for boundary value problems for first order multivalued differential systems. Our approach is based on topological transversality arguments, fixed point theorems and differential inequalities.

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