• Korean Journal of Mathematics
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• v.27 no.4
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• pp.879-898
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• 2019

In this paper we prove some interesting inclusions concerning the numerical range of some operators and the numerical range of theirs ranges with a convex function. Further, we prove some inequalities for the numerical radius. These inclusions and inequalities are based on some classical convexity inequalities for non-negative real numbers and some operator inequalities.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.359-376
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• 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.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.81-93
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• 2023

By utilizing a certain Libera integral operator considered on analytic multivalent functions in the unit disk U. Using the hypergeometric function and the Libera integral operator, we included a new convolution operator that expands on some previously specified operators in U, which broadens the scope of certain previously specified operators. We introduced and investigated the properties of new subclasses of functions f (z) ∈ A_p using this operator.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.491-502
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• 2005

The main purpose of this paper is to extend the exponentially convex functions which are defined and exponentially convex on a cylinderical neighborhood in the Heisenberg group. They are expanded in terms of an integral transform associated to the sub-Laplacian operator. Extension of such functions on abelian Lie group are studied in [15].

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.597-610
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• 2016

For a sufficiently adequate special case of the Dziok-Srivastava linear operator defined by means of the Hadamard product (or convolution) with Srivastava-Wright convolution operator, the authors investigate several mapping properties involving various subclasses of analytic and univalent functions, $G({\lambda},{\alpha})$ and $M({\lambda},{\alpha})$. Furthermore we discuss some inclusion relations for these subclasses to be in the classes of k-uniformly convex and k-starlike functions.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.371-381
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• 1997

Our basic concern in this paper is to investigate some geometric properties of the graph of a maximal monotone operator in the one dimensional case. Using a well-known theorem of Minty, we answer S. Simon's questions affirmatively in the one dimensional case. Further developments of these results are also treated. In addition, we provide a new proof of Rockafellar's characterization of maximal monotone operators on R: every maximal monotne operator from R to $2^R$ is the subdifferential of a proper convex lower semicontinuous function.

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

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.567-574
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• 2022

We use convolution techniques to define certain classes of starlike functions which are associated with Lommel operator. Some inclusion results are investigated. It is also shown that these classes are invariant under Bernardi integral operator.

• Kyungpook Mathematical Journal
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• v.53 no.1
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• pp.1-12
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• 2013

The purpose of the present paper is to obtain some subordination- and superordination-preserving properties for multivalent function associated the differintegral operators defined on the space of normalized analytic functions in the open unit disk. The sandwich type theorem for the integral operator is also considered.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.71-81
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• 2021

The main object of this present paper is to study some majorization problems for certain classes of analytic functions defined by means of q-calculus operator associated with exponential function.