Fixed points of multivalued ­θ-contractions on closed ball

Document Type : Original Article

Authors

1 Department of Mathematics, Taiz University, Taiz, Yemen.

2 Department of Mathematics, International Islamic University, H-10, Islamabad - 44000, Pakistan.

Abstract

We introduce the notion of multivalued θ-contractions on the closed ball and we obtain some new fixed point
results for such contractions. An example is given here to illustrate the usability of the obtained results.

Keywords


[1] H. A. HanCer, G. Minak, I. Altun, On a broad category of multivalued weakly Picard operators, Fixed Point
Theory. 18 (2017), 229-236.
[2] M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014 (2014), 8
pages.
[3] E. Kryeyszig, Introductory functional analysis with applications, John Wiley & Sons, New York, (1989). 1.10
[4] N. Mizoguchi, W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math.
Anal. Appl., 141 (1989), 177-188.
[5] G. Minak, I. Altun, Overall approach to Mizoguchi-Takahashi type fixed point results, Turk. J. Math., 40 (2016),
895-904.
[6] J. Nadler, Multivalued contraction mappings, paci c J. Math., 30 (1969), 475-478.
[7] S. Reich, Fixed points of contractive functions, Eoll. Un. Mat. Ital., 4 (1972), 26-42.
[8] F. Vetro, A generalization of Nadler fixed point theorem, Carpathian J. Math., 31 (2015), 403-410.