• Korean Journal of Mathematics
• /
• v.29 no.1
• /
• pp.91-103
• /
• 2021

In this paper we have established inequalities for a unified integral operator by using convexity of composition of two functions. The obtained results are directly connected to bounds of various fractional and conformable integral operators which are already known in literature. A generalized Hadamard integral inequality is obtained which further leads to its various versions for associated fractional integrals. Further, some implicated results are discussed.

• Korean Journal of Mathematics
• /
• v.29 no.1
• /
• pp.193-209
• /
• 2021

In this research, we offer two new quantum integral equalities for recently defined qε2-integral and derivative, the derived equalities then used to prove quantum integral inequalities of Simpson's and Newton's type for preinvex functions. We also considered the special cases of established results and offer several new and existing results inside the literature of Simpson's and Newton's type inequalities.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.2
• /
• pp.279-291
• /
• 2010

In this paper, we introduce the Kurzweil-Henstock-Pettis integral of fuzzy mappings in Banach spaces in terms of the Kurzweil-Henstock-Pettis integral of set-valued mappings and obtain some properties of the Kurzweil-Henstock-Pettis integral of fuzzy mappings in Banach spaces and the convergence theorem for Kurzweil-Henstock-Pettis integrable fuzzy mappings.

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.3
• /
• pp.535-541
• /
• 2005

In this paper, we define the ap-Denjoy integral and investigate some properties of the ap-Denjoy integral.

• Bulletin of the Korean Mathematical Society
• /
• v.41 no.1
• /
• pp.153-166
• /
• 2004

We prove the Radon-Nikodym theorem for a nonabsolute integral on measure spaces endowed with metric topologies and hence provide a descriptive definition of the integral.

• Honam Mathematical Journal
• /
• v.38 no.2
• /
• pp.231-241
• /
• 2016

In this paper we will define the tight integral closure of a finite set of ideals of a ring relative to a module and we will study some related results.

• Journal of the Chungcheong Mathematical Society
• /
• v.19 no.4
• /
• pp.299-312
• /
• 2006

In this paper, we introduce interior integral and prove uniform convergence theorems for the interior integral.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.1
• /
• pp.99-108
• /
• 2010

In this paper, we define the $M_{\alpha}$-integral and investigate properties of the $M_{\alpha}$-integral.

• Honam Mathematical Journal
• /
• v.38 no.1
• /
• pp.141-149
• /
• 2016

In this paper, we introduce and investigate the concept of Riemann Delta-alpha fractional integral on time scales. Many properties of this integral will be obtained.

• Korean Journal of Mathematics
• /
• v.18 no.3
• /
• pp.229-241
• /
• 2010

In this paper, we introduce the Denjoy-Pettis integral of fuzzy mappings in Banach spaces and obtain some properties of the Denjoy-Pettis integral of fuzzy mappings and the convergence theorems for Denjoy-Pettis integrable fuzzy mappings.