• Title/Summary/Keyword: compatible mappings

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COMMON FIXED POINTS FOR WEAKENED COMPATIBLE MAPPINGS SATISFYING THE GENERALIZED ϕ-WEAK CONTRACTION CONDITION

  • Jain, Deepak;Kumar, Sanjay;Jung, Chahn Yong
    • The Pure and Applied Mathematics
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    • v.26 no.2
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    • pp.99-110
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    • 2019
  • In this paper, we prove some common fixed point theorems for pairs of weakened compatible mappings (subcompatible and occasionally weakly compatible mappings) satisfying a generalized ${\phi}-weak$ contraction condition involving various combinations of the metric functions. In fact, our results improve the results of Jain et al.. Also we provide an example for validity of our results.

COMMON FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS WITHOUT CONTINUITY IN MENGER SPACES

  • Sharma, Sushil;Deshpande, Bhavana
    • The Pure and Applied Mathematics
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    • v.10 no.2
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    • pp.133-144
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    • 2003
  • The aim of this paper is to prove some common fixed point theorems for the class of compatible maps to larger class of weakly compatible maps without appeal to continuity in Monger spaces and we also give a set of alternative conditions in place of completeness of the space. We improve and extend the results of Dedeic & Sarapa [A common fixed point theorem for three mappings on Monger spaces. Math. Japon. 34 (1989), no. 6,919-923] and Rashwan & Hedar [On common fixed point theorems of compatible mappings in Monger spaces. Demonstratio Math. 31 (1998), no. 3, 537-546].

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FIXED POINTS OF ASYMPTOTICALLY REGULAR MAPPINGS

  • Kang, Shin-Min;Ronglu, Li
    • East Asian mathematical journal
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    • v.14 no.2
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    • pp.343-356
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    • 1998
  • In this paper, we prove some common fixed point theorems for compatible mappings by using asymptotically regular mappings under the contractive type of G. E. Hardy and T. D. Rogers, and also give some examples to illustrate our main theorems. Our results extend the results of M. D. Guay and K. L. Singh and others.

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COMMON FIXED POINTS FOR COMPATIBLE MAPPINGS OF TYPE(A) IN 2-METRIC SPACES

  • WANG, WEN-ZUO
    • Honam Mathematical Journal
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    • v.22 no.1
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    • pp.91-97
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    • 2000
  • In this paper we obtain a criterion for the existence of a common fixed point of a pair of mappings in 2-metric spaces. Our result generalizes a number of fixed point theorems given by Imdad, Khan and Khan [1], Kahn and Fisher [2], Kubiak [3], Rhoades [5], and Singh, Tiwari and Gupta [6].

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AN EXTENSION OF TELCI, TAS AND FISHER'S THEOREM

  • Lal, S.N.;Murthy, P.P.;Cho, Y.J.
    • Journal of the Korean Mathematical Society
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    • v.33 no.4
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    • pp.891-908
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    • 1996
  • Let (X,d) be a metric space and let T be a mapping from X into itself. We say that a metric space (X,d) is T-orbitally complete if every Cauchy sequence of the form ${T^{n_i}x}_{i \in N}$ for $x \in X$ converges to a point in X.

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FIXED POINT THEOREMS IN MENGER SPACES USING AN IMPLICIT RELATION

  • Chauhan, Sunny;Khan, M. Alamgir;Pant, B.D.
    • Honam Mathematical Journal
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    • v.35 no.4
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    • pp.551-564
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    • 2013
  • In 2008, Al-Thaga and Shahzad [Generalized I-nonexpansive selfmaps and invariant approximations, Acta Math. Sinica, 24(5) (2008), 867-876] introduced the notion of occasionally weakly compatible mappings in metric spaces. In this paper, we prove some common fixed point theorems for families of occasionally weakly compatible mappings in Menger spaces using an implicit relation. We also give an illustrative example to support our main result.

SOME FIXED POINT THEOREMS IN CONNECTION WITH TWO WEAKLY COMPATIBLE MAPPINGS IN BICOMPLEX VALUED METRIC SPACES

  • Choi, Junesang;Datta, Sanjib Kumar;Biswas, Tanmay;Islam, Md Nazimul
    • Honam Mathematical Journal
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    • v.39 no.1
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    • pp.115-126
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    • 2017
  • In this paper, we aim to prove certain common fixed point theorems for a pair of weakly compatible mappings satisfying (CLRg) (or (E.A)) property in the bicomplex valued metric spaces. We also provide some examples which support the main results here.

COUPLED FIXED POINT RESULTS IN G-FUZZY METRIC SPACES FOR WEAKLY COMPATIBLE MAPPINGS

  • Das, Krishnapada;Sarkar, Krishna Kanta
    • Korean Journal of Mathematics
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    • v.29 no.3
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    • pp.455-466
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    • 2021
  • Coupled fixed point results have attracted much attention among the researchers in recent times specially in the field of fuzzy metric spaces. In this paper we established a coupled fixed point result for weakly compatible mappings in G-fuzzy metric spaces. We have deduced a corollary to our main theorem. Our result also supported by examples.