Solutions to Fredholm Integral Inclusions via Generalized Fuzzy Contractions

Hamed H Al-Sulami, Jamshaid Ahmad, Nawab Hussain and Abdul Latif
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Hamed H Al-Sulami: Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Jamshaid Ahmad: Department of Mathematics, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia
Nawab Hussain: Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Abdul Latif: Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Mathematics, 2019, vol. 7, issue 9, 1-19

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 ) ) ? 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 ? 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 ?iri? by means of this new class of contractions. We also give a significantly non-trivial example to support our new results.

Keywords: fredholm integral inclusion; ?-fuzzy mappings; ?-contractions; fixed point; multivalued mappings (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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