• 호남수학학술지
• /
• 제42권2호
• /
• pp.359-376
• /
• 2020

The present research investigates the bounds of an integral operator for convex functions and a differentiable function f such that |f'| is convex. Further, these bounds of integral operators specifically produce estimations of various classical fractional and recently defined conformable integral operators. These results also contain bounds of Hadamard type for symmetric convex functions.

• Korean Journal of Mathematics
• /
• 제29권2호
• /
• pp.227-237
• /
• 2021

Opial inequality and its consequences are useful in establishing existence and uniqueness of solutions of initial and boundary value problems for differential and difference equations. In this paper we analyze Opial-type inequalities for convex functions. We have studied different versions of these inequalities for a generalized integral operator. Further difference of Opial-type inequalities are utilized to obtain generalized mean value theorems, which further produce various interesting derivations for fractional and conformable integral operators.

• Kyungpook Mathematical Journal
• /
• 제64권1호
• /
• pp.31-46
• /
• 2024

The aim of this paper is to present an approach to improve reverse Minkowski and Hölder-type inequalities using k-weighted fractional integral operators _a⁺𝔍^𝜇_w with respect to a strictly increasing continuous function 𝜇, by introducing two parameters of integrability, p and q. For various choices of 𝜇 we get interesting special cases.

• Korean Journal of Mathematics
• /
• 제29권1호
• /
• 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.