Generalized contraction principle

This paper deals with coincidence and fixed point theorems in minimal generalized convex spaces. By establishing a kind of KKM Principle in minimal generalized convex space, we obtain some results on coincidence point and fixed point theorems. Generalized versions of Ky Fan?s lemma, Fan-Browder fixed point theorem, Nash equilibrium theorem and some Urai?s type fixed point theorems in minimal generalized convex spaces are given.

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Fixed Point Theorems of Krasnosel’skii Type In Locally Convex Spaces and Applications to Integral Equations

Results in Mathematics ◽

10.1007/bf03323412 ◽

1994 ◽

Vol 25 (3-4) ◽

pp. 290-314 ◽

Cited By ~ 6

Author(s):

Le Hoan Hoa ◽

Klaus Schmitt

Keyword(s):

Fixed Point ◽

Integral Equations ◽

Fixed Point Theorems ◽

Locally Convex Spaces ◽

Locally Convex ◽

Convex Spaces

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Some Generalized Contraction Classes and Common Fixed Points in b-Metric Space Endowed with a Graph

Mathematics ◽

10.3390/math7080754 ◽

2019 ◽

Vol 7 (8) ◽

pp. 754 ◽

Cited By ~ 2

Author(s):

Reny George ◽

Hossam A Nabwey ◽

Rajagopalan Ramaswamy ◽

Stojan Radenović

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Metric Space ◽

Fixed Point Theorems ◽

Admissible Pair ◽

Common Fixed Points ◽

Multivalued Mappings ◽

Generalized Contraction ◽

Rational Contraction ◽

Common Fixed Point Theorems

We have introduced the new notions of R-weakly graph preserving and R-weakly α -admissible pair of multivalued mappings which includes the class of graph preserving mappings, weak graph preserving mappings as well as α -admissible mappings of type S, α * -admissible mappings of type S and α * - orbital admissible mappings of type S respectively. Some generalized contraction and rational contraction classes are also introduced for a pair of multivalued mappings and common fixed point theorems are proved in a b-metric space endowed with a graph. We have also applied our results to obtain common fixed point theorems for R-weakly α -admissible pair of multivalued mappings in a b-metric space which are the proper extension and generalization of many known results. Proper examples are provided in support of our results. Our main results and its consequences improve, generalize and extend many known fixed point results existing in literature.

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Set Contractions and KKM Mappings in Banach Spaces

Abstract and Applied Analysis ◽

10.1155/2013/346094 ◽

2013 ◽

Vol 2013 ◽

pp. 1-4

Author(s):

A. Razani ◽

N. Karamikabir

Keyword(s):

Fixed Point ◽

Banach Spaces ◽

Fixed Point Theorems ◽

Coincidence Theorems ◽

Kkm Mappings ◽

Contraction Maps

Some fixed point theorems for generalized set contraction maps and KKM type ones in Banach spaces are presented. Moreover, a new generalized set contraction is introduced. As an application, some coincidence theorems for KKM type set contractions are obtained.

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The Existence of Fixed Point Theorems via -Distance and -Admissible Mappings and Applications

Abstract and Applied Analysis ◽

10.1155/2013/165434 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8 ◽

Cited By ~ 3

Author(s):

Marwan Amin Kutbi ◽

Wutiphol Sintunavarat

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Common Fixed Point ◽

Binary Relation ◽

Point Theorem ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Coincidence Point ◽

Generalized Contraction ◽

Common Fixed Point Theorems

We introduce the concept of the generalized -contraction mappings and establish the existence of fixed point theorem for such mappings by using the properties of -distance and -admissible mappings. We also apply our result to coincidence point and common fixed point theorems in metric spaces. Further, the fixed point theorems endowed with an arbitrary binary relation are also derived from our results. Our results generalize the result of Kutbi, 2013, and several results in the literature.

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