• The Pure and Applied Mathematics
• /
• v.7 no.1
• /
• pp.1-6
• /
• 2000

An extension of $H\"{o}lder's$ inequality whose discrete form is described as follows is given. Let $\nu$ be a positive measure on a space Y, $\nu(Y)\;\neq\;0$, and let $f_{j}$(j = 1,2,...,n) be positive ν-integrable functions on Y. If ${\alpha}_j$ > 0(j = 1,2,...,n) and ${\beta}_j$(j = 1,2,...,k < n) are related to be (equation omitted) then (equation omitted).

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.2
• /
• pp.161-170
• /
• 2009

For various fuzzy numbers, many operations have been calculated. We generalize about triangular fuzzy number and calculate four operations based on the Zadeh's extension principle, addition A(+)B, subtraction A(-)B, multiplication A(${\cdot}$)B and division A(/)B for two generalized triangular fuzzy sets.

• East Asian mathematical journal
• /
• v.24 no.3
• /
• pp.213-221
• /
• 2008

In this paper, a new class of fuzzy topological spaces called ordered fuzzy pre-extremally disconnected spaces is introduced. Tietze extension theorem for ordered fuzzy pre-extremally disconnected spaces has been discussed as in [9] besides proving several other propositions and lemmas.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.11 no.3
• /
• pp.29-36
• /
• 2007

Let T be an ergodic measure preserving transformation on (X, B, ${\mu}$). It is called 2-simple if every 2-fold ergodic joining is either a product measure or an off-diagonal measure. In general, factors of simple maps are not simple. So far, there has been no characterization of the factor of simple maps. In this paper, we give a joining characterization of factors of simple maps.

• Communications of the Korean Mathematical Society
• /
• v.36 no.4
• /
• pp.705-714
• /
• 2021

The Whittaker function and its diverse extensions have been actively investigated. Here we aim to introduce an extension of the Whittaker function by using the known extended confluent hypergeometric function 𝚽_p,v and investigate some of its formulas such as integral representations, a transformation formula, Mellin transform, and a differential formula. Some special cases of our results are also considered.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.1
• /
• pp.217-224
• /
• 2021

In this paper, we study Ding injective modules over Frobenius extensions. Let R ⊂ A be a separable Frobenius extension of rings and M any left A-module, it is proved that M is a Ding injective left A-module if and only if M is a Ding injective left R-module if and only if A ⊗R M (HomR(A, M)) is a Ding injective left A-module.

• Journal of the Korean Mathematical Society
• /
• v.52 no.3
• /
• pp.649-661
• /
• 2015

Insertion-of-factors-property, which was introduced by Bell, has a role in the study of various sorts of zero-divisors in noncommutative rings. We in this note consider this property in the case that factors are restricted to maximal ideals. A ring is called IMIP when it satisfies such property. It is shown that the Dorroh extension of A by K is an IMIP ring if and only if A is an IFP ring without identity, where A is a nil algebra over a field K. The structure of an IMIP ring is studied in relation to various kinds of rings which have roles in noncommutative ring theory.

• Journal of Applied and Pure Mathematics
• /
• v.6 no.1_2
• /
• pp.21-36
• /
• 2024

In this paper, we study the existence of solutions for hybrid fractional differential equations with p-Laplacian operator involving fractional Caputo derivative of arbitrary order. This work can be seen as an extension of earlier research conducted on hybrid differential equations. Notably, the extension encompasses both the fractional aspect and the inclusion of the p-Laplacian operator. We build our analysis on a hybrid fixed point theorem originally established by Dhage. In addition, an example is provided to demonstrate the effectiveness of the main results.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.1951-1967
• /
• 2017

We aim to introduce a further extension of a family of the extended Hurwitz-Lerch Zeta functions of two variables. We then systematically investigate several interesting properties of the extended function such as its integral representations which provide extensions of various earlier corresponding results of two and one variables, its summation formula, its Mellin-Barnes type contour integral representations, its computational representation and fractional derivative formulas. A multi-parameter extension of the extended Hurwitz-Lerch Zeta function of two variables is also introduced. Relevant connections of certain special cases of the main results presented here with some known identities are pointed out.

• The Pure and Applied Mathematics
• /
• v.31 no.1
• /
• pp.1-19
• /
• 2024

In this paper, the notions of strong Connes amenability for certain products of Banach algebras and module extension of dual Banach algebras is investigated. We characterize χ ⊗ η-strong Connes amenability of projective tensor product ${\mathbb{K}}{\hat{\bigotimes}}{\mathbb{H}}$ via χ ⊗ η-σwc virtual diagonals, where χ ∈ 𝕂_* and η ∈ ℍ_* are linear functionals on dual Banach algebras 𝕂 and ℍ, respectively. Also, we present some conditions for the existence of (χ, θ)-σwc virtual diagonals in the θ-Lau product of 𝕂 ×_θ ℍ. Finally, we characterize the notion of (χ, 0)-strong Connes amenability for module extension of dual Banach algebras 𝕂 ⊕ 𝕏, where 𝕏 is a normal Banach 𝕂-bimodule.