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Fixed point theorems of G -fuzzy contractions in fuzzy metric spaces endowed with a graph

Satish Shukla (2014)

Communications in Mathematics

Let ( X , M , * ) be a fuzzy metric space endowed with a graph G such that the set V ( G ) of vertices of G coincides with X . Then we define a G -fuzzy contraction on X and prove some results concerning the existence and uniqueness of fixed point for such mappings. As a consequence of the main results we derive some extensions of known results from metric into fuzzy metric spaces. Some examples are given which illustrate the results.

Fixed Point Theorems of the Banach and Krasnosel’skii Type for Mappings on m -tuple Cartesian Product of Banach Algebras and Systems of Generalized Gripenberg’s Equations

Eva Brestovanská, Milan Medveď (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper we prove some fixed point theorems of the Banach and Krasnosel’skii type for mappings on the m -tuple Cartesian product of a Banach algebra X over . Using these theorems existence results for a system of integral equations of the Gripenberg’s type are proved. A sufficient condition for the nonexistence of blowing-up solutions of this system of integral equations is also proved.

Fixed point theory for multivalued maps in Fréchet spaces via degree and index theory

R.P. Agarwal, D. O'Regan, D.R. Sahu (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

New fixed point results are presented for multivalued maps defined on subsets of a Fréchet space E. The proof relies on the notion of a pseudo open set, degree and index theory, and on viewing E as the projective limit of a sequence of Banach spaces.

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