• Title, Summary, Keyword: common fixed point

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COMMON FIXED POINT RESULTS FOR NON-COMPATIBLE R-WEAKLY COMMUTING MAPPINGS IN PROBABILISTIC SEMIMETRIC SPACES USING CONTROL FUNCTIONS

  • Das, Krishnapada
    • Korean Journal of Mathematics
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    • v.27 no.3
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    • pp.629-643
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    • 2019
  • In common fixed point problems in metric spaces several versions of weak commutativity have been considered. Mappings which are not compatible have also been discussed in common fixed point problems. Here we consider common fixed point problems of non-compatible and R-weakly commuting mappings in probabilistic semimetric spaces with the help of a control function. This work is in line with research in probabilistic fixed point theory using control functions. Further we support our results by examples.

COMMON FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS IN MENGER SPACES

  • Sharma, S.;Choubey, K.
    • The Pure and Applied Mathematics
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    • v.10 no.4
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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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COMMON FIXED POINT THEOREMS FOR CONTRACTIVE TYPE MAPPINGS AND THEIR APPLICATIONS IN DYNAMIC PROGRAMMING

  • Liu, Zeqing;Wang, Lili;Kim, Hyeong-Kug;Kang, Shin-Min
    • Bulletin of the Korean Mathematical Society
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    • v.45 no.3
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    • pp.573-585
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    • 2008
  • A few sufficient conditions for the existence and uniqueness of fixed point and common fixed point for certain contractive type mappings in complete metric spaces are provided. Several existence and uniqueness results of solution and common solution for some functional equations and system of functional equations in dynamic programming are discussed by using the fixed point and common fixed point theorems presented in this paper.

RENARKS ON REWEAKLY COMMUTING MAPPONGS AND COMMON FIXED POINT THEOREMS

  • Pathak, H.-K;Cho, Y.-J;Kang, S.-M
    • Bulletin of the Korean Mathematical Society
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    • v.34 no.2
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    • pp.247-257
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    • 1997
  • It was the turning point in the "fixed point arena" when the notion of weak commutativity was introduced by Sessa [9] as a sharper tool to obtain common fixed points of mappings. As a result, all the results on fixed point theorems for commuting mappings were easily transformed in the setting of the new notion of weak commutativity of mappings. It gives a new impetus to the studying of common fixed points of mappings satisfying some contractive type conditions and a number of interesting results have been found by various authors. A bulk of results were produced and it was the centre of vigorous research activity in "Fixed Point Theory and its Application in various other Branches of Mathematical Sciences" in last two decades. A major break through was done by Jungck [3] when he proclaimed the new notion what he called "compatibility" of mapping and its usefulness for obtaining common fixed points of mappings was shown by him. There-after a flood of common fixed point theorems was produced by various researchers by using the improved notion of compatibility of mappings. of compatibility of mappings.

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Fixed point theorems for fuzzy mappings and applications

  • Lee, Byung-Soo;Cho, Yeol-Je;Jung, Jong-Soo
    • Communications of the Korean Mathematical Society
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    • v.11 no.1
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    • pp.89-108
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    • 1996
  • In this paper we obtain common fixed point theorems for sequences of fuzzy mappings on Menger probabilistic metric spaces, including common fixed point theorems for sequences of multi-valued mappings, which generalize and improve some results of Lee et al. [8] and Chang [2].

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COMMON FIXED POINTS OF WEAK-COMPATIBLE MAPS ON D-METRIC SPACE

  • Singh, Bijendra;Jain, Shobha
    • Journal of the Chungcheong Mathematical Society
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    • v.17 no.2
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    • pp.111-124
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    • 2004
  • In [4], Dhage proved a result for common fixed point of two self-maps satisfying a contractive condition in D-metric spaces. This note proves a fixed point theorem for five self-maps under weak-compatibility in D-metric space which improves and generalizes the above mentioned result.

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A common fixed point theorem in the intuitionistic fuzzy metric space (직관적 퍼지거리공간에서 공통 부동점 정리)

  • Park Jong-Seo;Kim Seon-Yu;Kang Hong-Jae
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • pp.71-74
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    • 2006
  • The purpose of this paper is to establish the common fixed point theorem in the intuitionistic fuzzy metric space in which it is a little revised in Park [11]. Our research are an extension of Jungck's common fixed point theorem [8] in the intuitionistic fuzzy metric space.

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