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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Abstract

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

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

Dates
First available in Project Euclid: 16 September 2015

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1442364588

Digital Object Identifier
doi:10.36045/bbms/1442364588

Mathematical Reviews number (MathSciNet)
MR3396992

Zentralblatt MATH identifier
1326.54046

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

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

Citation

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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