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Solutions to Fredholm Integral Inclusions via Generalized Fuzzy Contractions

Author

Listed:
  • 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)

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.

Suggested Citation

  • Hamed H Al-Sulami & Jamshaid Ahmad & Nawab Hussain & Abdul Latif, 2019. "Solutions to Fredholm Integral Inclusions via Generalized Fuzzy Contractions," Mathematics, MDPI, vol. 7(9), pages 1-19, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:808-:d:263284
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    References listed on IDEAS

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    1. Ravi P. Agarwal & Nawab Hussain & Mohamed-Aziz Taoudi, 2012. "Fixed Point Theorems in Ordered Banach Spaces and Applications to Nonlinear Integral Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, July.
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