E. S. Zhukovskii, E.A. Panasenko. On fixed points of multivalued mappings in spaces with a vector-valued metric ... P. 93-105

Nadler’s theorem on a fixed point of a multivalued mapping is extended to spaces with a vector-valued metric. A vector-valued metric is understood as a mapping with the properties of a usual metric and values in a linear normed ordered space. We prove an analog of Nadler’s theorem and apply it to a system of integral inclusions in a space of summable functions. Then we study a boundary value problem with multivalued conditions for systems of functional differential equations by means of reduction to a system of integral inclusions. Conditions for the existence of solutions are obtained and estimates of the solutions are given. The existence conditions do not contain the convexity requirement for the values of the multivalued function generating a Nemytskii operator.

Keywords: space with a vector-valued metric, contracting multivalued mapping, fixed point, integral inclusion.

The paper was received by the Editorial Office on October 9, 2017.

Funding Agency:

Ministry of Education and Science of the Russian Federation (project no. 3.8515.2017/БЧ);

Russian Foundation for Basic Research (projects no. 17-01-00553 and 16-01-00386);

Russian Science Foundation (project no. 17-11-01168).

Evgenii Semenovich Zhukovskiy, Dr. Phys.-Math. Sci., Prof., Research Institute of Mathematics,
Physics, and Computer Sciences, Tambov Derzhavin State University, Tambov, 392000 Russia;
Nikol’skii Mathematical Institute, RUDN University, Moscow, 117198 Russia,
e-mail: zukovskys@mail.ru .

Elena Aleksandrovna Panasenko, Cand. Sci. (Phys.-Math.), docent, Functional Analysis Department,
Tambov Derzhavin State University, Tambov, 392000 Russia,
e-mail: panlena_t@mail.ru .


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