• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.885-899
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• 2000

We obtain generalized versions of the Fan-Browder fixed point theorem for G-convex spaces. We define the class B of better admissible multimaps on G-convex spaces and show that any closed compact map in b fro ma locally G-convex uniform space into itself has a fixed point.

• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1205-1213
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• 2005

Applying a fixed point theorem for compact admissible maps due to Gorniewicz, we prove that under certain conditions each count ably condensing admissible maps in Frechet spaces has a positive eigenvalue. This result has many consequences, including the well-known theorem of Krasnoselskii.

• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.69-83
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• 2009

New Lefschetz fixed point theorems for compact absorbing contractive admissible maps between Frechet spaces are presented. Also we present new results for condensing maps with a compact attractor. The proof relies on fixed point theory in Banach spaces and viewing a Frechet space as the projective limit of a sequence of Banach spaces.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.4
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• pp.345-353
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• 2021

In this paper, first, we present new fixed point theorems for Mönch type multimaps on abstract convex uniform spaces and, also, a fixed point theorem for Mönch type multimaps in Hausdorff KKM L𝚪-spaces. Second, we show that Mönch type multimaps in the better admissible class defined on an L𝚪-space have fixed point properties whenever their ranges are Klee approximable. Finally, we obtain fixed point theorems on 𝔎ℭ-maps whose ranges are 𝚽-sets.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.307-313
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• 2005

The Lefschetz fixed point theorem is extended to compact continuous maps defined on an admissible subset of a Hausdorff topological space.

• Communications of the Korean Mathematical Society
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• v.24 no.2
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• pp.187-195
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• 2009

We investigate the boundary values of the holomorphic mean Lipschitz function. In fact, we prove that the admissible limit exists at every boundary point of the unit ball for the holomorphic mean Lipschitz functions under some assumptions on the Lipschitz order. Moreover, we get embedding theorems of holomorphic mean Lipschitz spaces into Hardy spaces or into the Bloch space on the unit ball in $\mathbb{C}_n$.

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.651-675
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• 2018

We present ${\alpha}$-type rational F-contractions in metric-like spaces, and respective fixed and common fixed point results for weakly ${\alpha}$-admissible mappings. Useful examples illustrate the effectiveness of the presented results. As applications, we obtain sufficient conditions for the existence of solutions of a certain type of integral equations followed by examples of nonlinear fractional differential equations that are verified numerically.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.383-394
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• 2023

In this paper, we shall introduce the new notions of ω-orbital admissible mappings, ω-interpolative Kannan type contraction and ω-interpolative Ciric-Reich-Rus type contraction. In the setting of these new contractions, we will prove some fixed point theorems in bipolar metric spaces. Some existing results from literature are also deduced from our main results. Some examples are also provided to illustrate the theorems.

• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.803-829
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• 1998

We give general fixed point theorems for compact multimaps in the "better" admissible class $B^{K}$ defined on admissible convex subsets (in the sense of Klee) of a topological vector space not necessarily locally convex. Those theorems are used to obtain results for $\Phi$-condensing maps. Our new theorems subsume more than seventy known or possible particular forms, and generalize them in terms of the involving spaces and the multimaps as well. Further topics closely related to our new theorems are discussed and some related problems are given in the last section.n.

• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.635-640
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• 2001

Let X be a T-admissible space and A(x) be the set of all admissible fibers at x∈X. In this paper, we introduce some basic concepts, properties, and known results about set-valued maps, hyperspaces and especially T-admissible spaces. And then, we construct a certain set-valued map(Theorem 2.3) and an arc from {x} to X∈A(x) in use of the set-valued maps(Theorem 2.3 through Theorem 2.7).