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Open AccessFeature PaperArticle

Fixed Points of Eventually Δ-Restrictive and Δ(ϵ)-Restrictive Set-Valued Maps in Metric Spaces

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Department of Applied Science and Humanities, Assam University, Silchar, Cachar, Assam 788011, India
2
Institute of Research and Development of Processes, University of the Basque Country, Campus of Leioa, 48940 Leioa (Bizakaia), Spain
*
Authors to whom correspondence should be addressed.
Symmetry 2020, 12(1), 127; https://doi.org/10.3390/sym12010127
Received: 22 December 2019 / Revised: 4 January 2020 / Accepted: 6 January 2020 / Published: 8 January 2020
The symmetry concept is an intrinsic property of metric spaces as the metric function generalizes the notion of distance between two points. There are several remarkable results in science in connection with symmetry principles that can be proved using fixed point arguments. Therefore, fixed point theory and symmetry principles bear significant correlation between them. In this paper, we introduce the new definition of the eventually Δ -restrictive set-valued map together with the concept of p-orbital continuity. Further, we introduce another new concept called the Δ ( ϵ ) -restrictive set-valued map. We establish several fixed point results related to these maps and proofs of these results also provide us with schemes to find a fixed point. In a couple of results, the stronger condition of compactness of the underlying metric space is assumed. Some results are illustrated with examples. View Full-Text
Keywords: fixed point; metric space; set-valued map; Δ(ϵ)-restrictive map; eventually Δ-restrictive map fixed point; metric space; set-valued map; Δ(ϵ)-restrictive map; eventually Δ-restrictive map
MDPI and ACS Style

Debnath, P.; de La Sen, M. Fixed Points of Eventually Δ-Restrictive and Δ(ϵ)-Restrictive Set-Valued Maps in Metric Spaces. Symmetry 2020, 12, 127.

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