General Topology-I

Fixed point of a ljubomir cirics quasi-contractionmapping in a generalized metric space

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.

/pdf/fixed-point-and-endpoint-theorems-for-set-valued-fuzzy-2munvpgy8u.pdf

Fixed point and endpoint theorems for set-valued fuzzy contraction maps in fuzzy metric spaces

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.

/pdf/fixed-points-of-suzuki-type-generalized-multivalued-mappings-58ulf9ouku.pdf

Fixed points of Suzuki type generalized multivalued mappings in fuzzy metric spaces with applications

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).

https://polipapers.upv.es/index.php/AGT/article/download/11417/11786

Ideals in B1(X) and residue class rings of B1(X) modulo an ideal

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.

/pdf/fixed-point-theorems-on-generalized-fuzzy-metric-spaces-5dgmk23xlm.pdf

Fixed Point Theorems on Generalized Fuzzy Metric Spaces

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.

https://polipapers.upv.es/index.php/AGT/article/download/10776/11208

On rings of Baire one functions

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...

Rings and subrings of continuous functions with countable range

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.

/pdf/further-on-fuzzy-pseudo-near-compactness-and-ps-ro-fuzzy-2rt86ilof9.pdf

A. Deb Ray

Papers

Fixed Point Theorems on Generalized Fuzzy Metric Spaces

Ideals in B1(X) and residue class rings of B1(X) modulo an ideal

On rings of Baire one functions

Rings and subrings of continuous functions with countable range

Further on Fuzzy Pseudo Near Compactness and ps-ro Fuzzy Continuous Functions