• Title/Summary/Keyword: compatible mappings of type (P)

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COMMON FIXED POINT THEOREMS FOR COMPATIBLE MAPPINGS OF TYPE (A) AND (P) WITH APPLICATIONS IN DYNAMIC PROGRAMMING

  • Jiang, Guojing;Liu, Min;Lee, Suk-Jin;Kang, Shin-Min
    • East Asian mathematical journal
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    • v.25 no.1
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    • pp.11-26
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    • 2009
  • In this paper, the concepts of compatible mappings of types (A) and (P) are introduced in an induced metric space, two common xed point theorems for two pairs of compatible mappings of types (A) and (P) in an induced complete metric space are established. As their applications, the existence and uniqueness results of common solution for a system of functional equations arising in dynamic programming are discussed.

COMPATIBLE MAPPINGS OF TYPE (I) AND (II) ON INTUITIONISTIC FUZZY METRIC SPACES IN CONSIDERATION OF COMMON FIXED POINT

  • Sharma, Sushil;Deshpande, Bhavana
    • Communications of the Korean Mathematical Society
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    • v.24 no.2
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    • pp.197-214
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    • 2009
  • In this paper, we formulate the definition of compatible mappings of type (I) and (II) in intuitionistic fuzzy metric spaces and prove a common fixed point theorem by using the conditions of compatible mappings of type (I) and (II) in complete intuitionistic fuzzy metric spaces. Our results intuitionistically fuzzify the result of Cho, Sedghi, and Shobe [4].

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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COMMON FIXED POINT THEOREMS OF MEIR-KEELER TYPE ON MULTIPLICATIVE METRIC SPACES

  • DESHPANDE, BHAVANA;SHEIKH, SAJAD AHMAD
    • The Pure and Applied Mathematics
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    • v.23 no.2
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    • pp.131-143
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    • 2016
  • In this paper, we present some common fixed point theorems for two pairs of weakly compatible self-mappings on multiplicative metric spaces satisfying a generalized Meir-Keeler type contractive condition. The results obtained in this paper extend, improve and generalize some well known comparable results in literature.

COMMON FIXED POINTS FOR COMPATIBLE MAPPINGS OF TYPE (P) AND AN APPLICATION IN DYNAMIC PROGRAMMING

  • Liu, Zeqing;Guo, Zhenyu;Kang, Shin-Min;Shim, Soo-Hak
    • Journal of applied mathematics & informatics
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    • v.26 no.1_2
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    • pp.61-73
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    • 2008
  • In this paper common fixed point theorems dealing with compatible mappings of type (P) are established. As a application, the existence and uniqueness of common solution for a system of functional equations arising in dynamic programming is given. The results presented in this paper improve, generalize and unify the corresponding results in this field.

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WEAK COMPATIBLE MAPPINGS OF TYPE (A) AND COMMON FIXED POINTS IN MENGER SPACES

  • Pathak, H.K.;Kang, S.M.;Baek, J.H.
    • Communications of the Korean Mathematical Society
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    • v.10 no.1
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    • pp.67-83
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    • 1995
  • The notion of probabilistic metric spaces (or statistical metric spaces) was introduced and studied by Menger [19] which is a generalization of metric space, and the study of these spaces was expanede rapidly with the pioneering works of Schweizer-Sklar [25]-[26]. The theory of probabilistic metric spaces is of fundamental importance in probabilistic function analysis. For the detailed discussions of these spaces and their applications, we refer to [9], [10], [28], [30]-[32], [36] and [39].

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EXISTENCE OF COINCIDENCE POINT UNDER GENERALIZED GERAGHTY-TYPE CONTRACTION WITH APPLICATION

  • Handa, Amrish
    • The Pure and Applied Mathematics
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    • v.27 no.3
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    • pp.109-124
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    • 2020
  • We establish coincidence point theorem for S-non-decreasing mappings under Geraghty-type contraction on partially ordered metric spaces. With the help of obtain result, we derive two dimensional results for generalized compatible pair of mappings F, G : X2 → X. As an application, we obtain the solution of integral equation and also give an example to show the usefulness of our results. Our results improve, sharpen, enrich and generalize various known results.

EMPLOYING α-ψ-CONTRACTION TO PROVE COUPLED COINCIDENCE POINT THEOREM FOR GENERALIZED COMPATIBLE PAIR OF MAPPINGS ON PARTIALLY ORDERED METRIC SPACES

  • Deshpande, Bhavana;Handa, Amrish
    • The Pure and Applied Mathematics
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    • v.25 no.2
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    • pp.73-94
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    • 2018
  • We introduce some new type of admissible mappings and prove a coupled coincidence point theorem by using newly defined concepts for generalized compatible pair of mappings satisfying ${\alpha}-{\psi}$ contraction on partially ordered metric spaces. We also prove the uniqueness of a coupled fixed point for such mappings in this setup. Furthermore, we give an example and an application to integral equations to demonstrate the applicability of the obtained results. Our results generalize some recent results in the literature.