Best Proximity Points for <i>p</i>–Cyclic Infimum Summing Contractions
Miroslav Hristov,
Atanas Ilchev,
Petar Kopanov,
Vasil Zhelinski,
Boyan Zlatanov
Affiliations
Miroslav Hristov
Department of Mathematical Analysis, Faculty of Mathematics and Informatics, Konstantin Preslavski University of Shumen, 115 Universitetska Str., 9700 Shumen, Bulgaria
Atanas Ilchev
Department of Real Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tsar Assen Str., 4000 Plovdiv, Bulgaria
Petar Kopanov
Department of Real Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tsar Assen Str., 4000 Plovdiv, Bulgaria
Vasil Zhelinski
Department of Real Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tsar Assen Str., 4000 Plovdiv, Bulgaria
Boyan Zlatanov
Department of Real Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tsar Assen Str., 4000 Plovdiv, Bulgaria
We investigate fixed points for p cyclic maps by introducing a new notion of p–cyclic infimum summing maps and a generalized best proximity point for p–cyclic maps. The idea generalizes some results about best proximity points in order to widen the class of sets and maps for which we can ensure the existence and uniqueness of best proximity points. The replacement of the classical notions of best proximity points and distance between the consecutive set arises from the well-known group traveling salesman problem and presents a different approach to solving it. We illustrate the new result with a map that does not satisfy the known results about best proximity maps for p–cyclic maps.
