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Solutions to Fredholm Integral Inclusions via Generalized Fuzzy Contractions.
- Source :
-
Mathematics (2227-7390) . Sep2019, Vol. 7 Issue 9, p808. 1p. - Publication Year :
- 2019
-
Abstract
- The aim of this study is to investigate the existence of solutions for the following Fredholm integral inclusion φ (t) ∈ f (t) + ∫ 0 1 K (t , s , φ (s)) ϱ s for t ∈ [ 0 , 1 ] , where f ∈ C [ 0 , 1 ] is a given real-valued function and K : [ 0 , 1 ] × [ 0 , 1 ] × R → K c v (R) a given multivalued operator, where K c v represents the family of non-empty compact and convex subsets of R , φ ∈ C [ 0 , 1 ] is the unknown function and ϱ is a metric defined on C [ 0 , 1 ] . To attain this target, we take advantage of fixed point theorems for α -fuzzy mappings satisfying a new class of contractive conditions in the context of complete metric spaces. We derive new fixed point results which extend and improve the well-known results of Banach, Kannan, Chatterjea, Reich, Hardy-Rogers, Berinde and Ćirić by means of this new class of contractions. We also give a significantly non-trivial example to support our new results. [ABSTRACT FROM AUTHOR]
- Subjects :
- *METRIC spaces
*FIXED point theory
*CONTRACTIONS (Topology)
*SET-valued maps
Subjects
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 7
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Mathematics (2227-7390)
- Publication Type :
- Academic Journal
- Accession number :
- 138966896
- Full Text :
- https://doi.org/10.3390/math7090808