Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 14 (2019), 1 -- 16

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This work is licensed under a Creative Commons Attribution 4.0 International License.

FIXED POINTS OF MULTIVALUED MAPPINGS IN METRIC SPACES

Binayak S. Choudhury, N. Metiya, S. Kundu and D. Khatua

Abstract. Admissibility of mappings are introduced to create conditions to minimally restrict various contractive conditions on pairs of points from a metric space in order to ensure fixed point property of the respective contractions. In the present work we define new admissibility conditions and control functions to obtain certain multivalued fixed point theorems. The corresponding single valued case is discussed. We define four weak contraction mappings of which two are multivalued and two are single valued. The results are without any assumption of continuity. There is an illustrative example.

2010 Mathematics Subject Classification: 54H10; 54H25; 47H10.
Keywords: Set valued analysis; Cyclic (α, β)-admissible mapping; Multivalued mapping; Fixed point.

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Binayak S. Choudhury
Department of Mathematics, Indian Institute of Engineering Science and Technology,
Shibpur, Howrah - 711103, West Bengal, India.
E-mail: binayak12@yahoo.co.in


Nikhilesh Metiya
Department of Mathematics, Sovarani Memorial College, Jagatballavpur,
Howrah-711408, West Bengal, India.
E-mail: metiya.nikhilesh@gmail.com


Sunirmal Kundu
Department of Mathematics, Government Degree College, Salboni,
Paschim Mednipur - 712516, West Bengal, India.
E-mail: sunirmalkundu2009@rediffmail.com


Debashis Khatua
Department of Mathematics, Indian Institute of Engineering Science and Technology,
Shibpur, Howrah - 711103, West Bengal, India.
E-mail: debashiskhatua@yahoo.com

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