• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.301-307
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• 2003

The purpose of this paper is to give a generalization of the quasi fixed-point theorem due to Lefebvre, and prove a new existence theorem of equilibrium in a generalized quasi-game.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.599-608
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• 2010

In this paper, we introduce the concept of generalized weak contractivity for set-valued maps defined on quasi metric spaces. We analyze the existence of fixed points for generalized weakly contractive set-valued maps. And we have Nadler's fixed point theorem and Banach's fixed point theorem in quasi metric spaces. We investigate the convergene of iterate schem of the form $x_{n+1}{\in}Fx_n$ with error estimates.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.1027-1035
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• 2011

In this paper, we introduce the concept of generalized weak q-contractivity for multivalued maps defined on quasi-metric spaces. A new fixed point theorem for these maps is established. The convergene of iterate schem of the form $x_n+1\;{\in}\;Fx_n$ is investigated. And a new periodic point theorem for weakly q-contractive self maps of quasi-metric spaces is proved.

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.93-104
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• 2024

In this paper, we will prove a fixed point theorem for self-mappings on a generalized quasi-ordered metric space which is a generalization of the concept of a generalized metric space with a partial order and we investigate a genralized quasi-ordered metric space related with fuzzy normed spaces. Further, we prove the stability of some functional equations in fuzzy normed spaces as an application of our fixed point theorem.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.491-502
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• 1998

We obtain new fixed point theorems on maps defined on "locally G-convex" subsets of a generalized convex spaces. Our first theorem is a Schauder-Tychonoff type generalization of the Brouwer fixed point theorem for a G-convex space, and the second main result is a fixed point theorem for the Kakutani maps. Our results extend many known generalizations of the Brouwer theorem, and are based on the Knaster-Kuratowski-Mazurkiewicz theorem. From these results, we deduce new results on collectively fixed points, intersection theorems for sets with convex sections and quasi-equilibrium theorems.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.4
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• pp.279-288
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• 2023

We obtain a Chandrabhan type fixed point theorem for a multimap having a non-compact domain and a weakly closed graph, and taking convex values only on a quasi-convex subset of Hausdorff locally convex topological vector space. We introduce the definition of Chandrabhan-set and find a sufficient condition for every countably condensing multimap to have a relatively compact Chandrabhan-set. Finally, we establish a new version of Sadovskii fixed point theorem for multimaps.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.915-929
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• 2020

We prove a fixed point theorem for generalized asymptotic pointwise nonexpansive mapping in the setting of a hyperbolic space. A one-step iterative scheme approximating common fixed point of two generalized asymptotic pointwise (quasi-) nonexpansive mappings in this setting is provided. We obtain ∆-convergence and strong convergence theorems of the iterative scheme for two generalized asymptotic pointwise nonexpansive mappings in the same setting. Our results generalize and extend some related results in the literature.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.691-700
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• 2009

We use the fixed alternative theorem to establish Hyers-Ulam-Rassias stability of the quadratic functional equation where functions map a linear space into a complete quasi p-normed space. Moreover, we will show that the continuity behavior of an approximately quadratic mapping, which is controlled by a suitable continuous function, implies the continuity of a unique quadratic function, which is a good approximation to the mapping. We also give a few applications of our results in some special cases.

• Communications of the Korean Mathematical Society
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• v.24 no.4
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• pp.523-528
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• 2009

In this paper, we consider the existence of solutions to some generalized vector quasi-equilibrium-like problem under a c-diagonal quasi-convexity assumptions, but not monotone concepts. For an example, in the proof of Theorem 1, the c-diagonally quasi-convex concepts of a set-valued mapping was used but monotone condition was not used. Our problem is a new kind of equilibrium problems, which can be compared with those of Hou et al. [4].

• Journal of the Chungcheong Mathematical Society
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• v.20 no.1
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• pp.59-64
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• 2007

In this paper, we will introduce the generalized operator equlibrium problem and generalized operator quasi-equlibrium problem which generalize operator equlibrium problem due to Kazmi and Raouf into multi-valued and quasi-equlibrium problems. Using a Park's fixed point theorem, we will prove a new existence theorem on generalized operator equlibrium problem which serves as a basic existence theorem for various kinds of nonlinear problems.