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2 Demonstratio Mathematica

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Noncyclic Meir-Keeler contractions and best proximity pair theorems

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Gabeleh M. , Markin J.

Demonstratio Mathematica

2018

tom Vol. 51, nr 1

171--181

In this article, we consider the class of noncyclic Meir-Keeler contractions and study the existence and convergence of best proximity pairs for such mappings in the setting of complete CAT(0) spaces. We also discuss asymptotic pointwise noncyclic Meir-Keeler contractions in the framework of uniformly convex Banach spaces and generalize a main result of Chen [Chen C. M., A note on asymptotic pointwise weaker Meir-Keeler type contractions, Appl. Math. Lett., 2012, 25, 1267-1269]. Examples are given to support our main results.

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

100%

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.