Ümran Başar
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Research Interests
Ümran Başar has a total of 1 co-authors. Here are the top co-authors by number of shared publications:
- Ishak Altun
Department of Mathematics, Faculty of Engineering and Natural Science, Kirikkale University, 71450 Yahsihan, Kirikkale, Turkey
2 shared publications
Latest Publications
- Open Access
- 9 April 2026
- Published by Springer Nature in Journal of Fixed Point Theory and Applications
- Vol. 28 (2) , 35
On set-valued convex contractions
In this paper, we introduce and study a new class of multivalued mappings called set-valued convex contractions of order two . This notion extends the classical concept of Nadler contractions by incorporating two control parameters that jointly govern the contractive behavior of the mapping through both the Pompeiu–Hausdorff metric and the underlying metric of the space. We establish a fixed point theorem for such mappings in complete metric spaces under the assumption of upper semicontinuity. Our result properly generalizes Nadler’s fixed point theorem and provides a unified framework encompassing several existing types of multivalued contractions. Illustrative examples are provided to demonstrate that the new class of contractions is strictly broader than the classical one. Possible extensions and applications of the main result to more general metric-like spaces are also discussed.
- 9 April 2026
- Published by Springer Nature in Journal of Fixed Point Theory and Applications
- Vol. 28 (2) , 35
Open AccessOn set-valued convex contractions
In this paper, we introduce and study a new class of multivalued mappings called set-valued convex contractions of order two . This notion extends the classical concept of Nadler contractions by incorporating two control parameters that jointly govern the contractive behavior of the mapping through both the Pompeiu–Hausdorff metric and the underlying metric of the space. We establish a fixed point theorem for such mappings in complete metric spaces under the assumption of upper semicontinuity. Our result properly generalizes Nadler’s fixed point theorem and provides a unified framework encompassing several existing types of multivalued contractions. Illustrative examples are provided to demonstrate that the new class of contractions is strictly broader than the classical one. Possible extensions and applications of the main result to more general metric-like spaces are also discussed.
- Open Access
- 29 January 2026
- Published by Springer Nature in Journal of Fixed Point Theory and Applications
- Vol. 28 (1) , 14
Almost weakly picard operators
In the present paper, we will introduce and exemplify the class of almost weakly Picard operator, taking into account some weak forms of the Picard operators, which is one of the most important concepts of metric fixed point theory, available in the literature. Then, we will present a fixed point theorem that shows that this new class is not meaningless by developing the concept of “mapping contracting perimeters of triangles” recently defined by Petrov. Finally, we will define the concept of $$(\phi ,L)$$ -contractive perimeters of triangles using comparison functions and show that such mappings are weakly Picard operators in the complete metric space.- 29 January 2026
- Published by Springer Nature in Journal of Fixed Point Theory and Applications
- Vol. 28 (1) , 14
Open AccessAlmost weakly picard operators
In the present paper, we will introduce and exemplify the class of almost weakly Picard operator, taking into account some weak forms of the Picard operators, which is one of the most important concepts of metric fixed point theory, available in the literature. Then, we will present a fixed point theorem that shows that this new class is not meaningless by developing the concept of “mapping contracting perimeters of triangles” recently defined by Petrov. Finally, we will define the concept of $$(\phi ,L)$$ -contractive perimeters of triangles using comparison functions and show that such mappings are weakly Picard operators in the complete metric space.