Bulletin of the Belgian Mathematical Society - Simon Stevin

Recent developments about multivalued weakly Picard operators

Gülhan Minak, Ishak Altun, and Salvador Romaguera

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In the present paper, considering a recent technique, which is used by Wardowski [24] for fixed points of single-valued mappings, we give a new and general class of multivalued weakly Picard operators on complete metric spaces and show that the class of multivalued almost contractions (both linear and nonlinear cases in the sense of Berinde and Berinde [9]) is a proper subset of this new class. We also give a nontrivial example showing this fact.

Article information

Bull. Belg. Math. Soc. Simon Stevin, Volume 22, Number 3 (2015), 411-422.

First available in Project Euclid: 16 September 2015

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 54H25: Fixed-point and coincidence theorems [See also 47H10, 55M20]
Secondary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]

Multivalued weakly Picard operator multivalued almost $F$-contraction fixed point


Minak, Gülhan; Altun, Ishak; Romaguera, Salvador. Recent developments about multivalued weakly Picard operators. Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 3, 411--422. doi:10.36045/bbms/1442364588. https://projecteuclid.org/euclid.bbms/1442364588

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