Solutions to Fredholm Integral Inclusions via Generalized Fuzzy Contractions

Clicks: 156
ID: 274534
2019
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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.
Reference Key
al-sulami2019mathematicssolutions Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Hamed H Al-Sulami;Jamshaid Ahmad;Nawab Hussain;Abdul Latif;Al-Sulami, Hamed H;Ahmad, Jamshaid;Hussain, Nawab;Latif, Abdul;
Journal Mathematics
Year 2019
DOI
10.3390/math7090808
URL
https://www.mdpi.com/2227-7390/7/9/808/htm
Keywords
fixed point fredholm integral inclusion α-fuzzy mappings Θ-contractions multivalued mappings

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