Dr. Sirajo Yahaya of School of Arts& Sciences, and others Proved a Fixed Point of
Dr. Sirajo Yahaya, an Assistant Professor of Mathematics and Statistics in the School of Arts and Sciences at the American University of Nigeria (AUN), Yola, and two other researchers from Ahmadu Bello University, Zaria, have recently published their findings. The paper titled “Fixed points of bilateral multivalued contractions” was published in FILOMAT, Volume 38, Issue 8, on March 8, 2024. FILOMAT is the journal of the Faculty of Sciences and Mathematics, University of Niš, Serbia, in Southeast Europe.
In the paper, the concepts of ‘Jaggi, Dass-Gupta, and Caristi-Ciri ́’s c-type bilateral multivalued’ contractions are introduced in the framework of metric spaces, and new conditions for the existence of fixed points for such contractions are analyzed. A few consequences in single-valued mappings, which include the conclusion of the main result of Chen et al. on bilateral contractions, [Mathematics, 2019, 7, 538], are obtained. In addition, nontrivial examples are provided to support the validity of the results obtained.
The ideas being discussed in the setting of metric spaces are completely fundamental. Hence, they can be improved upon when presented in the framework of generalized metric spaces such as b-metric spaces, F-metric spaces, and some other pseudo-metric or quasi-metric spaces.
Moreover, the paper broadened the scope of the fixed-point theory of multivalued mappings by incorporating bilateral approaches. To this end, Jaggi-type bilateral multivalued contraction, Dass-Gupta-type bilateral multivalued contraction and Ciric-Caristi-type multivalued contraction are initiated, and the corresponding fixed point theorems are proved, with examples illustrating the hypotheses of the main results.
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Reported by John Abah