Fixed Point And Coupled Fixed Point Theorems For Multivalued Contractions With Respect To The Excess Functional

Authors

1 Faculty of Mathematics and Computer Science, Babe¸ s-Bolyai University Cluj-Napoca, Romania.

2 Faculty of Business, Babe¸ s-Bolyai University Cluj-Napoca, Romania.

Abstract

In this paper, we will consider the coupled fixed point problem for a multi-valued operator satisfying a
contraction condition with respect to the excess functional in b-metric spaces. The approach is based
on a fixed point theorem for a multi-valued operator in the setting of a b-metric space. On one hand,
we will consider the problem of the existence of the solutions and on the other hand, data dependence,
well-posedness, Ulam-Hyers stability and limit shadowing property of the coupled fixed point problem are
discussed. Some applications to a system of integral inclusions and to a multi-valued periodic boundary
value problem are also given. c

Keywords


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