Existence and Approximation of Fixed Points of Enriched φ -Contractions in Banach Spaces

Vasile Berinde (), Jackie Harjani and Kishin Sadarangani
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Vasile Berinde: Department of Mathematics and Computer Science, Technical University of Baia Mare, North University Center at Baia Mare, 430122 Baia Mare, Romania
Jackie Harjani: Department of Mathematics, Universidad de Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain
Kishin Sadarangani: Department of Mathematics, Universidad de Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain

Mathematics, 2022, vol. 10, issue 21, 1-16

Abstract: We introduce the class of enriched φ -contractions in Banach spaces as a natural generalization of φ -contractions and study the existence and approximation of the fixed points of mappings in this new class, which is shown to be an unsaturated class of mappings in the setting of a Banach space. We illustrated the usefulness of our fixed point results by studying the existence and uniqueness of the solutions of some second order ( p , q ) -difference equations with integral boundary value conditions.

Keywords: Banach space; enriched ? -contraction; enriched cyclic ? -contraction; fixed point; Maia type fixed point theorem; ( p , q )-difference equation; integral boundary value condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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