• Title/Summary/Keyword: weak-compatible maps

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On Fixed Point Theorem of Weak Compatible Maps of Type(γ) in Complete Intuitionistic Fuzzy Metric Space

  • Park, Jong-Seo
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.11 no.1
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    • pp.38-43
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    • 2011
  • In this paper, we give definitions of compatible mappings of type(${\gamma}$) in intuitionistic fuzzy metric space and obtain common fixed point theorem under the conditions of weak compatible mappings of type(${\gamma}$) in complete intuitionistic fuzzy metric space. Our research generalize, extend and improve the results given by Sedghi et.al.[12].

COMMON FIXED POINTS OF A WEAK-COMPATIBLE PAIR OF A SINGLE VALUED AND A MULTIVALUED MAPS IN D-METRIC SPACES

  • Singh, Bijendra;Jain, Shobha
    • Journal of the Chungcheong Mathematical Society
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    • v.18 no.1
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    • pp.51-64
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    • 2005
  • The object of this paper is to prove two unique common fixed point theorems for a pair of a set-valued map and a self map satisfying a general contractive condition using orbital concept and weak-compatibility of the pair. One of these results generalizes substantially, the result of Dhage, Jennifer and Kang [4]. Simultaneously, its implications for two maps and one map improves and generalizes the results of Dhage [3], and Rhoades [11]. All the results of this paper are new.

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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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FIXED POINT THEOREMS VIA FAMILY OF MAPS IN WEAK NON-ARCHIMEDEAN MENGER PM-SPACES

  • Singh, Deepak;Ahmed, Amin
    • The Pure and Applied Mathematics
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    • v.20 no.3
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    • pp.181-198
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    • 2013
  • C. Vetro [4] gave the concept of weak non-Archimedean in fuzzy metric space. Using the same concept for Menger PM spaces, Mishra et al. [22] proved the common fixed point theorem for six maps, Also they introduced semi-compatibility. In this paper, we generalized the theorem [22] for family of maps and proved the common fixed point theorems using the pair of semi-compatible and reciprocally continuous maps for one pair and R-weakly commuting maps for another pair in Menger WNAPM-spaces. Our results extends and generalizes several known results in metric spaces, probabilistic metric spaces and the similar spaces.

COMMON FIXED POINTS OF A LIMIT WEAK COMPATIBLE PAIR OF A MULTIVALUED MAPPING AND A SINGLE VALUED MAPPING IN D-METRIC SPACES

  • Singh, Bijendra;Jain, Shobha;jain, Shishir
    • East Asian mathematical journal
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    • v.22 no.1
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    • pp.35-51
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    • 2006
  • This paper deals with a general contraction. Two fixed-point theorems for a limit weak-compatible pair of a multi-valued map and a self map on a D-metric space have been established. These results improve significantly, the main results of Dhage, Jennifer and Kang [5] by reducing its assumption and generalizing its contraction simultaneously. At the same time some results of Singh, Jain and Jain [12] are generalized from a self map to a pair of a set-valued and a self map. Theorems of Veerapandi and Rao [16] get generalized and improved by these results. All the results of this paper are new.

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SEMI-COMPATIBILITY AND FIXED POINTS OF EXPANSION MAPPINGS IN 2-METRIC SPACES

  • Singh, Bijendra;Jain, Shobha
    • Journal of the Chungcheong Mathematical Society
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    • v.17 no.2
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    • pp.125-136
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    • 2004
  • This paper introduces the notion of semi-compatible self-maps in 2-metric spaces and establishes a fixed point theorem for four self-maps, satisfying an implicit relation through semi-compatibility of a pair of self-maps. This results in another fixed point theorem for four expansion maps which generalizes and improves many results of Kang et. al. [5] with an application.

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WEAKER FORMS OF COMMUTING MAPS AND EXISTENCE OF FIXED POINTS

  • Singh, S.L.;Tomar, Anita
    • The Pure and Applied Mathematics
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    • v.10 no.3
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    • pp.145-161
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    • 2003
  • Weak commutativity of a pair of maps was introduced by Sessa [On a weak commutativity condition of mappings in fixed point considerations. Publ. Inst. Math. (Beograd) (N.S.) 32(40) (1982),149-153] in fixed point considerations. Thereafter a number of generalizations of this notion has been obtained. The purpose of this paper is to present a brief development of weaker forms of commuting maps, and to obtain two fixed point theorems for noncommuting and noncontinuous maps on noncomplete metric spaces.

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COMMON FIXED POINTS WITHOUT CONTINUITY IN FUZZY METRIC SPACES

  • SHARMA SUSHIL;DESHPANDE BHAVANA
    • The Pure and Applied Mathematics
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    • v.12 no.4 s.30
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    • pp.289-306
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    • 2005
  • The aim of this paper is to prove some common fixed point theorems for six discontinuous mappings in non complete fussy metric spaces with condition of weak compatibility.

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