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Common fixed point and periodic point results in multiplicative metric spaces

100%
Nazir T., Silvestrov S.
Waves, Wavelets and Fractals
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2017
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tom 3
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nr 1
61-74
EN
In this paper, we study the common fixed point and periodic point results for self-mapings in the setup of multiplicative metric spaces. We also study the well-posedness of these obtained our results. We also study the common fixed point results of mappings involved in the cyclic representation. Moreover, some applications to obtain the common solution of integral equations are presented.
2
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Fuzzy fixed point results with rational type contractions in partially ordered complex-valued metric spaces

86%
Sarwar M., Humaira H., Huang H.
Commentationes Mathematicae
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2018
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tom 58
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nr 1-2
EN
In this manuscript, some fixed point results for fuzzy mappings with rational type contraction in the context of a complete partially ordered complex-valued metric space are established. The derived results generalize some fixed point theorems in the existing literature. An appropriate example is given.
3
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Fixed point properties for semigroups of nonexpansive mappings on convex sets in dual Banach spaces

86%
Lau A. T.-M., Zhang Y.
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
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2018
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tom 17
4
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On common fixed point theorems for semi-compatible mappings in Menger space

86%
Singh B., Jain A., Lodha B.
Commentationes Mathematicae
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2010
|
tom 50
|
nr 2
EN
In this paper, the concept of semi-compatibility and weak compatibility in Menger space has been applied to prove a common fixed point theorem for six self maps. Our result generalizes and extends the result of Pathak and Verma [6].
5
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On the Existence of Common Fixed Points for Semigroups of Nonlinear Mappings in Modular Function Spaces

72%
Kozlowski W. M.
Commentationes Mathematicae
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2011
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tom 51
|
nr 1
EN
Let \(C\) be a \(\rho\)-bounded, \(\rho\)-closed, convex subset of a modular function space \(L_\rho\). We investigate the existence of common fixed points for semigroups of nonlinear mappings \(T_t\colon C\to C\), i.e. a family such that \(T_0(x) = x\), \(T_{s+t} = T_s (T_t (x))\), where each \(T_t\) is either \(\rho\)-contraction or \(\rho\)-nonexpansive. We also briefly discuss existence of such semigroups and touch upon applications to differential equations.
6
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On the construction of common fixed points for semigroups of nonlinear mappings in uniformly convex and uniformly smooth Banach spaces

58%
Kozlowski W. M.
Commentationes Mathematicae
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2012
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tom 52
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nr 2
EN
Let \(C\) be a bounded, closed, convex subset of a uniformly convex and uniformly smooth Banach space \(X\). We investigate the weak convergence of the generalized Krasnosel'skii-Mann and Ishikawa iteration processes to common fixed points of semigroups of nonlinear mappings \(T_t\colon C \to C\). Each of \(T_t\) is assumed to be pointwise Lipschitzian, that is, there exists a family of functions \(\alpha_t\colon C \to [0, \infty)\) such that \(\|T_t(x) - T_t (y)\| \leq\alpha_t (x)\|x -y\|\) for \(x, y \in C\). The paper demonstrates how the weak compactness of \(C\) plays an essential role in proving the weak convergence of these processes to common fixed points.
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