• 제목/요약/키워드: Fixed point theorems

검색결과 427건 처리시간 0.023초

EXTENSIONS OF ORDERED FIXED POINT THEOREMS

  • Sehie Park
    • Nonlinear Functional Analysis and Applications
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    • 제28권3호
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    • pp.831-850
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    • 2023
  • Our long-standing Metatheorem in Ordered Fixed Point Theory is applied to some well-known order theoretic fixed point theorems. In the first half of this article, we introduce extended versions of the Zermelo fixed point theorem, Zorn's lemma, and the Caristi fixed point theorem based on the Brøndsted-Jachymski principle and our 2023 Metatheorem. We show some of their applications to other fixed point theorems or theorems on the existence of maximal elements in partially ordered sets. In the second half, we collect and improve order theoretic fixed point theorems in the collection of Howard-Rubin in 1991 and others. In fact, we improve or extend several ordering principles or fixed point theorems due to Brézis-Browder, Brøndsted, Knaster-Tarski, Tarski-Kantorovitch, Turinici, Granas-Horvath, Jachymski, and others.

FIXED POINT THEOREMS ON GENERALIZED CONVEX SPACES

  • Kim, Hoon-Joo
    • 대한수학회지
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    • 제35권2호
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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.

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COINCIDENCE POINT AND FIXED POINT THEOREMS IN PARTIAL METRIC SPACES FOR CONTRACTIVE TYPE MAPPINGS WITH APPLICATIONS

  • SALUJA, G.S.;KIM, JONG KYU;LIM, WON HEE
    • Journal of applied mathematics & informatics
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    • 제40권5_6호
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    • pp.1053-1071
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    • 2022
  • The purpose of this article is to establish some fixed point theorems, a common fixed point theorem and a coincidence point theorem via contractive type condition in the framework of complete partial metric spaces and give some examples in support of our results. As an application to the results, we give some fixed point theorems for integral type contractive conditions. The results presented in this paper extend and generalize several results from the existing literature.

FIXED POINTS OF WEAKLY INWARD 1-SET-CONTRACTION MAPPINGS

  • Duan, Huagui;Xu, Shaoyuan;Li, Guozhen
    • 대한수학회지
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    • 제45권6호
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    • pp.1725-1740
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    • 2008
  • In this paper, we introduce a fixed point index of weakly inward 1-set-contraction mappings. With the aid of the new index, we obtain some new fixed point theorems, nonzero fixed point theorems and multiple positive fixed points for this class of mappings. As an application of nonzero fixed point theorems, we discuss an eigenvalue problem.

FIXED POINT THEOREMS FOR MӦNCH TYPE MAPS IN ABSTRACT CONVEX UNIFORM SPACES

  • Kim, Hoonjoo
    • 충청수학회지
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    • 제34권4호
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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.

FIXED POINT THEOREMS IN FUZZY METRIC SPACES FOR MAPPINGS WITH SOME CONTRACTIVE TYPE CONDITIONS

  • Patir, Bijoy;Goswami, Nilakshi;Mishra, Lakshmi Narayan
    • Korean Journal of Mathematics
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    • 제26권2호
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    • pp.307-326
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    • 2018
  • In this paper, we derive some fixed point theorems in fuzzy metric spaces for self mappings satisfying different contractive type conditions. Some of these theorems generalize some results of Wairojjana et al. (Fixed Point Theory and Applications (2015) 2015:69). Several examples in support of the theorems are also presented here.

NOTE FOR THE TRIPLED AND QUADRUPLE FIXED POINTS OF THE MIXED MONOTONE MAPPINGS

  • Wu, Jun;Liu, Yicheng
    • 대한수학회보
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    • 제50권3호
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    • pp.993-1005
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    • 2013
  • In this paper, to include more generalized cases, the authors present a modified concept for the tripled and quadruple fixed point of the mixed monotone mappings. Also, they investigate the existence and uniqueness of fixed point of the ordered monotone operator with the Matkowski contractive conditions in the partial ordered metric spaces. As the direct consequences, the existence of coupled fixed point, tripled fixed point and quadruple fixed point are explored at the common framework and some previous results in [T. G. Bhaskar and V. Lakshmikan-tham, Fixed point theory in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), 1379-1393; V. Berinde and M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011), no. 15, 4889-4897; E. Karapinar and N. V. Luong, Quadruple fixed point theorems for nonlinear contractions, Computers and Mathematics with Applications (2012), doi:10.1016/j.camwa.2012.02061] are improved. Finally, some fixed point theorems are proved.

COMMON FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS IN MENGER SPACES

  • Sharma, S.;Choubey, K.
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제10권4호
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    • pp.245-254
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    • 2003
  • In this paper we prove common fixed point theorems for four mappings, under the condition of weakly compatible mappings in Menger spaces, without taking any function continuous. We improve results of [A common fixed point theorem for three mappings on Menger spaces. Math. Japan. 34 (1989), no. 6, 919-923], [On common fixed point theorems of compatible mappings in Menger spaces. Demonstratio Math. 31 (1998), no. 3, 537-546].

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