• 제목/요약/키워드: Banach's fixed point theorem

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SOME RESULTS ON FIXED POINTS IN THE FUZZY METRIC SPACE

  • RAZANI ABDOLRAHMAN;SHIRDARYAZDI MARYAM
    • Journal of applied mathematics & informatics
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    • 제20권1_2호
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    • pp.401-408
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    • 2006
  • Fixed point theory is one of famous theories from theoretical and numerical point of views. Banach fixed point theorem plays a main role in this theory. In this article, Grabiec's fuzzy Banach contraction theorem [3] and Vasuki's theorem [12] for a complete fuzzy metric space, in the sense of Song [11] (or George and Veeramani), is proved by an extra condition.

CONTROLLABILITY OF SECOND ORDER SEMILINEAR VOLTERRA INTEGRODIFFERENTIAL SYSTEMS IN BANACH SPACES

  • Balachandran, K.;Park, J.Y.;Anthoni, S.-Marshal
    • 대한수학회보
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    • 제36권1호
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    • pp.1-13
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    • 1999
  • Sufficient conditions for controllability of semilinear second order Volterra integrodifferential systems in Banach spaces are established using the theory of strongly continuous cosine families. The results are obtained by using the Schauder fixed point theorem. An example is provided to illustrate the theory.

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FIXED POINT THEOREMS FOR INFINITE DIMENSIONAL HOLOMORPHIC FUNCTIONS

  • Harris, Lwarence-A.
    • 대한수학회지
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    • 제41권1호
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    • pp.175-192
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    • 2004
  • This talk discusses conditions on the numerical range of a holomorphic function defined on a bounded convex domain in a complex Banach space that imply that the function has a unique fixed point. In particular, extensions of the Earle-Hamilton Theorem are given for such domains. The theorems are applied to obtain a quantitative version of the inverse function theorem for holomorphic functions and a distortion form of Cartan's unique-ness theorem.

A WEAK COMMON FIXED POINT THEOREM IN NORMED ALMOST LINEAR SPACES

  • Lee, Sang-Han
    • Journal of applied mathematics & informatics
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    • 제4권2호
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    • pp.573-581
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    • 1997
  • In this paper we prove a weak common fixed point theo-rem in a normed almost linear space which is different from the result of S. P. Singh and B.A. Meade [9]. However for a Banach X our theorem is equal to the result of S. P. Singh and B. A. Meade.

ON THE SOLVABILITY OF A NONLINEAR LANGEVIN EQUATION INVOLVING TWO FRACTIONAL ORDERS IN DIFFERENT INTERVALS

  • Turab, Ali;Sintunavarat, Wutiphol
    • Nonlinear Functional Analysis and Applications
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    • 제26권5호
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    • pp.1021-1034
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    • 2021
  • This paper deals with a nonlinear Langevin equation involving two fractional orders with three-point boundary conditions. Our aim is to find the existence of solutions for the proposed Langevin equation by using the Banach contraction mapping principle and the Krasnoselskii's fixed point theorem. Three examples are also given to show the significance of our results.

EXTENSIONS OF BANACH'S AND KANNAN'S RESULTS IN FUZZY METRIC SPACES

  • Choudhur, Binayak S.;Das, Krishnapada;Das, Pradyut
    • 대한수학회논문집
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    • 제27권2호
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    • pp.265-277
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    • 2012
  • In this paper we establish two common fixed point theorems in fuzzy metric spaces. These theorems are generalisations of the Banach contraction mapping principle and the Kannan's fixed point theorem respectively in fuzzy metric spaces. Our result is also supported by examples.

FIXED POINT THEOREMS FOR SET-VALUED MAPS IN QUASI-METRIC SPACES

  • Cho, Seong-Hoon
    • 충청수학회지
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    • 제23권4호
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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.