Taiwanese Journal of Mathematics

ON A NEW CLASS OF MULTIVALUED WEAKLY PICARD OPERATORS ON COMPLETE METRIC SPACES

Ishak Altun, Murat Olgun, and Gülhan Mınak

Full-text: Open access

Abstract

In the present paper, the concept of nonlinear $F$-contraction formultivalued mappings in metric spaces is introduced and considering the new proof technique, which was used for single valued maps by Wardowski [D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012, 2012:94, 6 pp.], we demonstrate that multivalued nonlinear $F$-contractions of Ćirić type are weakly Picard operators on complete metric spaces. Finally, we give a nontrivial example to guarantee that our result is veritable generalization of recent result of Ćirić [Lj. B. Ćirić, Multi-valued nonlinear contraction mappings, Nonlinear Analysis, 71 (2009), 2716-2723]. Also, we show that many fixed point results in the literature can not be applied to this example.

Article information

Source
Taiwanese J. Math., Volume 19, Number 3 (2015), 659-672.

Dates
First available in Project Euclid: 4 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499133655

Digital Object Identifier
doi:10.11650/tjm.19.2015.4752

Mathematical Reviews number (MathSciNet)
MR3353246

Zentralblatt MATH identifier
1357.54029

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

Keywords
weakly Picard operator fixed point multivalued mappings nonlinear $F$-contractions complete metric space

Citation

Altun, Ishak; Olgun, Murat; Mınak, Gülhan. ON A NEW CLASS OF MULTIVALUED WEAKLY PICARD OPERATORS ON COMPLETE METRIC SPACES. Taiwanese J. Math. 19 (2015), no. 3, 659--672. doi:10.11650/tjm.19.2015.4752. https://projecteuclid.org/euclid.twjm/1499133655


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References

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