Author

# A. Deb Ray

Other affiliations: West Bengal State University

Bio: A. Deb Ray is an academic researcher from University of Calcutta. The author has contributed to research in topics: Mathematics & Fuzzy logic. The author has an hindex of 4, co-authored 22 publications receiving 39 citations. Previous affiliations of A. Deb Ray include West Bengal State University.

##### Papers

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TL;DR: A generalized fuzzy metrics space is defined and shown to be a proper generalization of a fuzzy metric space and the results corresponding to Banach's and Ciric's fixed point theorems are obtained under the postulates.

Abstract: In this paper, a generalized fuzzy metric space is defined and shown to be a proper generalization of a fuzzy metric space. Besides, the results corresponding to Banach’s and Ciric’s fixed point theorems are obtained under our postulates.

13 citations

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TL;DR: In this paper, the duality between ideals of the ring B 1 (X) of all real valued Baire one functions on a topological space X and typical families of zero sets, called Z B -filters, was explored.

Abstract: This paper explores the duality between ideals of the ring B 1 (X) of all real valued Baire one functions on a topological space X and typical families of zero sets, called Z B -filters, on X. As a natural outcome of this study, it is observed that B 1 (X) is a Gelfand ring but non-Noetherian in general. Introducing fixed and free maximal ideals in the context of B 1 (X), complete descriptions of the fixed maximal ideals of both B 1 (X) and B 1 * (X) are obtained. Though free maximal ideals of B 1 (X) and those of B 1 * (X) do not show any relationship in general, their counterparts, i.e., the fixed maximal ideals obey natural relations. It is proved here that for a perfectly normal T 1 space X, free maximal ideals of B 1 (X) are determined by a typical class of Baire one functions. In the concluding part of this paper, we study residue class ring of B 1 (X) modulo an ideal, with special emphasize on real and hyper real maximal ideals of B 1 (X).

9 citations

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TL;DR: In this paper, the ring of real valued Baire one functions, denoted by B 1 (X) and B ∗ 1(X) was introduced and several analogous results, especially an analogue of Urysohn's extension theorem was established.

Abstract: This paper introduces the ring of all real valued Baire one functions, denoted by B 1 (X) and also the ring of all real valued bounded Baire one functions, denoted by B ∗ 1 (X). Though the resemblance between C(X) and B 1 (X) is the focal theme of this paper, it is observed that unlike C(X) and C ∗ (X) (real valued bounded continuous functions), B ∗ 1 (X) is a proper subclass of B 1 (X) in almost every non-trivial situation. Introducing B 1 -embedding and B ∗ 1 -embedding, several analogous results, especially, an analogue of Urysohn’s extension theorem is established.

7 citations

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TL;DR: In this paper, the intermediate rings of the functionally countable subalgebra of C(X) (i.e., the rings Ac(X), lying between Cc∗ (X) and Cc(X)), where X is a Hausdor zero-dimensional space, are studied.

Abstract: Intermediate rings of the functionally countable subalgebra of C(X) (i.e., the rings Ac(X) lying between Cc∗(X) and Cc(X)), where X is a Hausdorﬀ zero-dimensional space, are studied in this article...

4 citations

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TL;DR: Main objective of this paper is to study further properties of fuzzy pseudo near compactness via ps-ro closed fuzzy sets, fuzzy nets and fuzzy filterbases and it is shown by an example that Ps-ro fuzzy continuous and fuzzy continuous functions do not imply each other.

Abstract: Main objective of this paper is to study further properties of fuzzy pseudo near compactness via ps-ro closed fuzzy sets, fuzzy nets and fuzzy filterbases. It is shown by an example that ps-ro fuzzy continuous and fuzzy continuous functions do not imply each other. Several characterizations of ps-ro fuzzy continuous function are obtained in terms of a newly introduced concept of ps-ro interior operator, ps-ro q-nbd and its graph.

3 citations

##### Cited by

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01 Jan 2002

41 citations

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TL;DR: By presenting an endpoint result, a fixed point theorem for set-valued fuzzy contraction type maps in complete fuzzy metric spaces is presented which extends and improves some well-know results in literature.

Abstract: In this paper, we first present a fixed point theorem for set-valued fuzzy contraction type maps in complete fuzzy metric spaces which extends and improves some well-know results in literature. Then by presenting an endpoint result we initiate endpoint theory for fuzzy contraction maps in fuzzy metric spaces.

29 citations

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TL;DR: In this paper, the authors introduce a class of multivalued mappings satisfying a Suzuki type generalized contractive condition in the framework of fuzzy metric spaces and present fixed point results for such mappings.

Abstract: The aim of this paper is to introduce a class of multivalued mappings satisfying a Suzuki type generalized contractive condition in the framework of fuzzy metric spaces and to present fixed point results for such mappings. Some examples are presented to support the results proved herein. As an application, a common fixed point result for a hybrid pair of single and multivalued mappings is obtained. We show the existence and uniqueness of a common bounded solution of functional equations arising in dynamic programming. Our results generalize and extend various results in the existing literature.

24 citations

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TL;DR: In this paper, the duality between ideals of the ring B 1 (X) of all real valued Baire one functions on a topological space X and typical families of zero sets, called Z B -filters, was explored.

Abstract: This paper explores the duality between ideals of the ring B 1 (X) of all real valued Baire one functions on a topological space X and typical families of zero sets, called Z B -filters, on X. As a natural outcome of this study, it is observed that B 1 (X) is a Gelfand ring but non-Noetherian in general. Introducing fixed and free maximal ideals in the context of B 1 (X), complete descriptions of the fixed maximal ideals of both B 1 (X) and B 1 * (X) are obtained. Though free maximal ideals of B 1 (X) and those of B 1 * (X) do not show any relationship in general, their counterparts, i.e., the fixed maximal ideals obey natural relations. It is proved here that for a perfectly normal T 1 space X, free maximal ideals of B 1 (X) are determined by a typical class of Baire one functions. In the concluding part of this paper, we study residue class ring of B 1 (X) modulo an ideal, with special emphasize on real and hyper real maximal ideals of B 1 (X).

9 citations