Some New Extensions of Multivalued Contractions in a b-metric Space and Its Applications

Reny George and Hemanth Kumar Pathak
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Reny George: Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
Hemanth Kumar Pathak: SOS in Mathematics, Pt. Ravishankar Shukla University, Raipur 492010, India

Mathematics, 2020, vol. 9, issue 1, 1-21

Abstract: The H β -Hausdorff–Pompeiu b-metric for β ∈ [ 0 , 1 ] is introduced as a new variant of the Hausdorff–Pompeiu b-metric H . Various types of multi-valued H β -contractions are introduced and fixed point theorems are proved for such contractions in a b-metric space. The multi-valued Nadler contraction, Czervik contraction, q-quasi contraction, Hardy Rogers contraction, weak quasi contraction and Ciric contraction existing in literature are all one or the other type of multi-valued H β -contraction but the converse is not necessarily true. Proper examples are given in support of our claim. As applications of our results, we have proved the existence of a unique multi-valued fractal of an iterated multifunction system defined on a b-metric space and an existence theorem of Filippov type for an integral inclusion problem by introducing a generalized norm on the space of selections of the multifunction.

Keywords: b-metric space; H ? -Hausdorff–Pompeiu b-metric; multi-valued fractal; iterated multifunction system; integral inclusion (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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