Volume 32, No. 1 (2022)

HYPER CHROMATIC AND AUGMENTED CHROMATIC ZAGREB INDICES OF WHEEL RELATED GRAPHS AND CYCLE RELATED GRAPHS

B. BASAVANAGOUD(1), GOUTAM VEERAPUR(2)

In this paper, we introduce the chromatic variance of a graph. This notion is a counterpart for the variance of a graph introduced by F. K. Bell. Here, in the setting of graph color-ing, the role played by the degrees of graph vertices is replaced by the products between the indices of colors and the cardinality of the corresponding color class. We compute the chromatic variance, the hyper chromatic and augmented chromatic Zagreb indices of wheel related graphs and cycle related graphs.

APPLICATIONS OF fπg-CLOSED SETS IN FUZZY TOPOLOGICAL SPACES

ANJANA BHATTACHARYYA

In [8], fuzzy π-closed sets are introduced. Using this concept as a basic tool, in [9] the notion of fuzzy π generalized closed set (fπg-closed set, for short) is introduced and stud-ied. Afterwards, a new type of generalized version of fuzzy closure operator, viz., fπg-closure operator is introduced which is an idempotent operator. Next we introduce a new type of generalized version of fuzzy open and closed-like functions, viz., fπg-open and fπg-closed functions and we characterize these two functions by using fπg-closure operator. Next we introduce fπg-continuous function and fπg-irresolute function. Then we introduce two new types of separation axioms, viz., fπg-regularity, fπg-normality and a new type of compactness, viz., fπg-compactness. It is shown that under fπg-irresolute function, fπg-regularity, fπg-normality and fπg-compactness remain invari-ant. Lastly, a new of fuzzy T2-space, viz., fπg-T2 space is introduced and it is shown that inverse image of fuzzy T2-space [20] (resp., fπg-T2 space) under fπg-continuous (resp., fπg-irresolute) function is an fπg-T2 space.

DETERMINANT INEQUALITIES FOR POSITIVE DEFINITE MATRICES VIA BHATIA AND KITTANEH-MANASRAH RESULTS

SILVESTRU SEVER DRAGOMIR

In this paper we prove among others that, if A and B are positive definite matrices, then [the following inequality holds]: 0& \leq \int_{0}^{1}\left[ \det \left( \left( 1-t\right) A+tB\right) \right] ^{-1}dt-\left[ \det \left( \frac{A+B}{2}\right) \right] ^{-1} \\ & \leq \frac{1}{3}\left[ \frac{1}{2}\left( \left[ \det \left( A\right) % \right] ^{-1}+\left[ \det \left( B\right) \right] ^{-1}\right) -\left[ \det \left( \frac{A+B}{2}\right) \right] ^{-1}\right] \\ & \leq \frac{1}{2}\left( \left[ \det \left( A\right) \right] ^{-1}+\left[ \det \left( B\right) \right] ^{-1}\right) -\int_{0}^{1}\left[ \det \left( \left( 1-t\right) A+tB\right) \right] ^{-1}dt \\ & \leq \frac{4}{3}\left[ \frac{1}{2}\left( \left[ \det \left( A\right) % \right] ^{-1}+\left[ \det \left( B\right) \right] ^{-1}\right) -\left[ \det \left( \frac{A+B}{2}\right) \right] ^{-1}\right] .

UPPER AND LOWER (τ, M)-J-CONTINUOUS MULTIFUNCTIONS

TAKASHI NOIRI(1), VALERIU POPA(2)

We introduce the notions of upper/lower (τ, m)-J-continuous multifunctions and obtain many characterizations of such multifunctions. The notion is obtained from a multifunc-tion F :(X, τ ) → (Y, σ, J) and several generalizations of J-open sets on the ideal topological space (Y, σ, J). If F is single valued, m = σ and J = {∅}, then the above multifunction is a (τ, m)-continuous function.

ANOTHER MENON-TYPE IDENTITY DERIVED FROM GROUP ACTIONS

MARIUS TĂRNĂUCEANU

In this short note, we give a new Menon-type identity involving the sum of element or-ders and the sum of cyclic subgroup orders of a finite abelian group. This is based on the weighted form of Burnside’s lemma applied to the action of the power automorphism group.