Geodesic
On some enriched contractions in Banach spaces and an application
Filomat, Tome 35 (2021) no. 15, p. 5017

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DOI

In this paper, we introduce two new types of enriched contractions, viz., enriched A-contraction and enriched A-contraction. Then we obtain fixed points of mappings satisfying such contractions using the fixed point property of the average operator of the mappings. Further, we study the well-posedness and limit shadowing property of the fixed point problem involving the contractions, and give some examples to validate the results proved. Our work improves Berinde and Păcurar's recent results on different kinds enriched contractions and some well known classical fixed point results. As an application, we prove an existence and uniqueness theorem for an integro-differential equation
DOI : 10.2298/FIL2115017M
Classification : 47H05, 47H10, 54H25
Keywords: Banach spaces, enriched A-contraction, enriched A′-contraction, well-posedness, limit shadowing property 
Pratikshan Mondal; Hiranmoy Garai; Lakshmi Kanta Dey. On some enriched contractions in Banach spaces and an application. Filomat, Tome 35 (2021) no. 15, p. 5017 . doi: 10.2298/FIL2115017M
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     title = {On some enriched contractions in {Banach} spaces and an application},
     journal = {Filomat},
     pages = {5017 },
     year = {2021},
     volume = {35},
     number = {15},
     doi = {10.2298/FIL2115017M},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2115017M/}
}
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