Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 17 (2022), 205 -- 223

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

COUPLED FIXED POINT SETS WITH DATA-DEPENDENCE AND STABILITY

Binayak S. Choudhury, Nikhilesh Metiya and Sunirmal Kundu

Abstract. In this paper we establish a coupled fixed point theorem of a coupled multivalued mapping defined on a complete metric space. In our result we use a new contractive inequality. There are rational terms in the expression of the inequality. The contractive condition on the nonlinear map is assumed only to hold on the elements that are related by a binary relation. The main theorem has several corollaries and is illustrated with example. The main result is deduced in metric spaces. Its consequences are discussed for α- admissible mapping as well as in metric spaces with partial order and graph respectively.

2020 Mathematics Subject Classification: 54H10, 54H25, 47H10.
Keywords: Metric space; Hausdorff distance; Binary relation; Dominated map; Coupled fixed point; Data dependence; Stability.

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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 General Degree College, Salboni,
Paschim Mednipur - 721516, West Bengal, India.
E-mail: sunirmalkundu2009@rediffmail.com



http://www.utgjiu.ro/math/sma