• Kyungpook Mathematical Journal
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• v.28 no.1
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• pp.79-82
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• 1988

This paper investigates the relationship between compactness and pseudo-compactness in subsets of C(X) where X is locally compact and first countable. Two primary theorems are proven. First, equicontinuity at a point is proven to be equivalent to the existence of a certain open cover of a pseudo-compact subset of C(X). The second theorem proves the equivalence of compactness and pseudo-compctness for closed subsets F of C(X).

• Kyungpook Mathematical Journal
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• v.53 no.2
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• pp.257-271
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• 2013

In this article, we establish the existence of at least three unbounded positive solutions to a boundary-value problem of the nonlinear singular fractional differential equation. Our analysis relies on the well known fixed point theorems in the cones.

• The Pure and Applied Mathematics
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• v.10 no.3
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• pp.145-161
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• 2003

Weak commutativity of a pair of maps was introduced by Sessa [On a weak commutativity condition of mappings in fixed point considerations. Publ. Inst. Math. (Beograd) (N.S.) 32(40) (1982),149-153] in fixed point considerations. Thereafter a number of generalizations of this notion has been obtained. The purpose of this paper is to present a brief development of weaker forms of commuting maps, and to obtain two fixed point theorems for noncommuting and noncontinuous maps on noncomplete metric spaces.

• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.461-489
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• 2006

In this article, we establish the existence theorem for measure-valued Dyson series and show that it satisfies the Volterra-type integral equation. Furthermore, we prove the stability theorems for measure-valued Dyson series.

• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.411-427
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• 2019

The existence, uniqueness and iterative approximations of fixed points for some contractive mappings of integral type defined in complete metric spaces with w-distance are proved. Four examples are given to demonstrate that the results in this paper extend and improve some well-known results in the literature.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.581-591
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• 2021

In this paper, we discuss and investigate the existence of the inclusion L^p(.),𝜃 (𝜇) ⊆ L^q(.),𝜃 (𝜈), where 𝜇 and 𝜈 are two finite measures on (X, Σ). Moreover, we show that the generalized variable exponent grand Lebesgue space L^p(.),𝜃 (Ω) has a potential-type approximate identity, where Ω is a bounded open subset of ℝ^d.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.227-237
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• 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.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.4
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• pp.429-444
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• 2020

For a quadrilateral P, we consider the centroid G0 of the vertices of P, the perimeter centroid G1 of the edges of P and the centroid G2 of the interior of P, respectively. It is well known that P satisfies G0 = G1 or G0 = G2 if and only if it is a parallelogram. In this paper, we investigate various quadrilaterals satisfying G1 = G2. As a result, we establish some characterization theorems. One of them asserts the existence of convex quadrilaterals satisfying G1 = G2 without symmetry.

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.581-600
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• 2021

In this paper we obtain a unique common fixed point theorem for four self-maps which are involved in (𝜙, 𝜓)-weak contraction of a partially ordered b-metric space. The necessary condition has been given to a space for the existence of an unique common fixed of the maps. And our work changed conditions and nonlinear contraction, and search for the unique common fixed point of the maps.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1423-1438
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• 2022

In this paper, we study a special exhaustion function on almost Hermitian manifolds and establish the existence result by using the Hessian comparison theorem. From the viewpoint of the exhaustion function, we establish a related Schwarz type lemma for almost holomorphic maps between two almost Hermitian manifolds. As corollaries, we deduce several versions of Schwarz and Liouville type theorems for almost holomorphic maps.