Solution to Fredholm integral inclusions via (F, δ_b )-contractions

Abstract

We present sufficient conditions for the existence of solutions of Fredholm integral inclusion equations using new sort of contractions, named as multivalued almost F -contractions and multivalued almost F -contraction pairs under ı-distance, defined in b-metric spaces. We give its relevance to fixed point results in orbitally complete b-metric spaces. To rationalize the notions and outcome, we illustrate the appropriate examples.

Notes on Some Recent Papers Concerning $F$-Contractions in $b$-Metric Spaces

“…Further, their approach was used in the papers [1,2,8,10,11,12,13,14,15,16] to obtain various fixed point results, mostly for multivalued mappings. However, as we are going to show using the following result, most of the conditions used in all these articles are too strong.…”

Multivalued FG-Contraction Mappings on Directed Graphs

“…In this section we are going to apply the obtained results to the problem of existence of solutions for a Fredholm-type integral inclusion. Problems of this kind were treated by several researchers, see, e.g., [15,17,18].…”

Fixed Point Results for Hybrid Rational Contractions under a New Compatible Condition with an Application

“…In 2012, Aydi and co-authors [7,8] demonstrated fixed point and common fixed point theorems for set-valued quasi-contraction mappings and set-valued weak φ-contraction mappings within the framework of b-metric spaces. Various papers have explored fixed point theory for both single-valued and set-valued operators in b-metric spaces, as documented in references [9][10][11][12][13][14][15][16][17][18][19].…”