In this paper, we define pre compact set in intuitionistic fuzzymetric spaces and prove that any subset of an intuitionistic fuzzy metric space is compact if and only if it is pre compact and complete. Also we define topologically complete intuitionistic fuzzy metrizable spaces and prove that any G δ set in a complete intuitionistic fuzzy metric spaces is a topologically complete intuitionistic fuzzy metrizable space and vice versa.

On the Intuitionistic Fuzzy Metric Spaces

In this paper, we show that every surjective n-homomorphism (n-anti-homomorphism) from a Banach algebra A into a semisimple Ba- nach algebra B is continuous.

AUTOMATIC CONTINUITY OF SURJECTIVE n-HOMOMORPHISMS ON BANACH ALGEBRAS

/pdf/n-jordan-homomorphisms-on-commutative-algebras-2gb5gppfna.pdf

n-Jordan homomorphisms on commutative algebras

In the present work we solve the problem of finding the fuzzy distance between two subsets of a fuzzy metric space for which we use a non-self fuzzy contraction mapping from one set to the other. It is a fuzzy extension of the proximity point problem and, by its nature, is a problem of global optimization. The contraction is defined here with the help of two control functions. We define a geometric property of the fuzzy metric space. The main result is illustrated with an example. Our result extends a fuzzy version of the Banach contraction mapping principle.

http://yujor.fon.bg.ac.rs/index.php/yujor/article/download/627/625

Determining Fuzzy Distance Through Non-Self Fuzzy Contractions

We show that every Banach algebra $${\mathcal {A}}$$ is 3-Jordan functionally continuous. More especially, every 3-Jordan homomorphism from a Banach algebra $${\mathcal {A}}$$ into a commutative semisimple Banach algebra $${\mathcal {B}}$$ is automatically continuous. We also prove the same result for n-Jordan homomorphism ($$n\geqslant 4$$) with the additional hypothesis that the Banach algebra $${\mathcal {A}}$$ is unital. A characterization of n-Jordan homomorphism for the special case $$n\in \lbrace 2,3,4\rbrace $$ is also given.

Characterization of n-Jordan Homomorphisms and Automatic Continuity of 3-Jordan Homomorphisms on Banach Algebras

Click on the link to view the abstract. Keywords: Automatic continuity; Banach algebras; semisimple; strongly semisimple; factorizable algebras; n -homomorphism Quaestiones Mathematicae 33(2010), 189–196

Automatic Continuity of N-Homomorphisms between Banach Algebras

In this paper, we dene the concepts of commute proximally, dominate prox- imally, weakly dominate proximally and common best proximity point in fuzzy metric space (abbreviated, FM -space). We prove some common best proximity point and com- mon xed point theorems for dominate proximally and weakly dominate proximally map- pings in FM -space under certain conditions. Our results generalize many known results in metric space.

Some results on common best proximity point in fuzzy metric

In this paper, we define the concepts of commute proximally, domi- nate proximally, weakly dominate proximally and common best proximity point in fuzzy metric space (abbreviated, FM-space). We prove some common best prox- imity point and common fixed point theorems for dominate proximally and weakly dominate proximally mappings in FM-space under certain conditions. Our results generalize many known results in metric space.

Some results on common best proximity point in fuzzy metric spaces

We extend the notion of homomorphisms and characters to $$n$$
 -homomorphisms and $$n$$
 -characters on algebras, and then show that some properties of characters are also valid for $$n$$
 -characters on commutative $$lmc$$
 topological algebras, and the space of continuous $$n$$
 -characters $$M_{(A,n)}$$
 is relatively compact in $$A'$$
 (the dual space of $$A$$
 ), with the weak* topology (Gelfand topology), whenever $$A$$
 is a commutative $$lmc$$
 $$Q$$
 -algebra. We also find relations between characters, $$n$$
 -characters, and continuous $$n$$
 -characters on commutative Frechet algebras. Let $$B$$
 be a topological algebra and $$(A_{\alpha },\varphi _{\beta \alpha })$$
 (resp. $$(A_{\alpha },\varphi _{\alpha \beta })$$
 ) be an inductive system (resp. a projective system) of topological algebras. Then we obtain relations between $$n-Hom(A_{\alpha },B)$$
 and $$n-Hom(A,B)$$
 , or between , the inductive limit, and $$M_{(A,n)}$$
 , where , is the inductive limit (resp. $$A=\varprojlim A_{\alpha }$$
 , is the projective limit) and $$n-Hom(A_{\alpha },B)$$
 (resp. $$n-Hom(A,B)$$
 ), is the space of all continuous n-homomorphisms from $$A_\alpha $$
 (resp. $$A$$
 ) into $$B$$
 .

/pdf/certain-properties-of-n-characters-and-n-homomorphisms-on-40alm6j0yc.pdf

Certain Properties of n-Characters and n-Homomorphisms on Topological Algebras

In this paper, we define the concepts of commute proximally, dominate proximally, weakly dominate proximally, proximal generalized φ-contraction and common best proximity point in probabilistic Menger space. We prove some common best proximity point and common fixed point theorems for dominate proximally and weakly dominate proximally mappings in probabilistic Menger space under certain conditions. Finally we show that proximal generalized φ-contractions have best proximity point in probabilistic Menger space. Our results generalize many known results in metric space.

Some results on common best proximity point and common fixed point theorem in probabilistic menger space

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