Extended suprametric spaces and Stone-type theorem

Sumati Kumari Panda; Ravi P Agarwal; Erdal Karapínar; Sumati Kumari Panda; Ravi P Agarwal; Erdal Karapínar

doi:10.3934/math.20231179

AIMS Mathematics

2023, Volume 8, Issue 10: 23183-23199. doi: 10.3934/math.20231179

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Extended suprametric spaces and Stone-type theorem

1.
Department of Mathematics, GMR Institute of Technology, Rajam-532127, Andhra Pradesh, India
2.
Department of Mathematics, Texas A & M University-Kingsville 700 University Blvd., MSC 172 Kingsville, Texas 78363-8202
3.
Department of Medical Research, China Medical University Hospital, China Medical University, 40402, Taichung, Taiwan
4.
Department of Mathematics, Çankaya University, 06790, Etimesgut, Ankara, Turkey

Received: 28 March 2023 Revised: 01 July 2023 Accepted: 13 July 2023 Published: 20 July 2023
MSC : 47H10, 54E35, 54E99

Extended suprametric spaces are defined, and the contraction principle is established using elementary properties of the greatest lower bound instead of the usual iteration procedure. Thereafter, some topological results and the Stone-type theorem are derived in terms of suprametric spaces. Also, we have shown that every suprametric space is metrizable. Further, we prove the existence of a solution of Ito-Doob type stochastic integral equations using our main fixed point theorem in extended suprametric spaces.
- an extended suprametric space,
- metrization,
- fixed point and Ito-Doob type stochastic integral equations
Citation: Sumati Kumari Panda, Ravi P Agarwal, Erdal Karapínar. Extended suprametric spaces and Stone-type theorem[J]. AIMS Mathematics, 2023, 8(10): 23183-23199. doi: 10.3934/math.20231179

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Abstract

Extended suprametric spaces are defined, and the contraction principle is established using elementary properties of the greatest lower bound instead of the usual iteration procedure. Thereafter, some topological results and the Stone-type theorem are derived in terms of suprametric spaces. Also, we have shown that every suprametric space is metrizable. Further, we prove the existence of a solution of Ito-Doob type stochastic integral equations using our main fixed point theorem in extended suprametric spaces.

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