A new type of contractive multivalued operators

The aim of this paper is to introduce a new type of multivalued operators similar to those of Kikkawa–Suzuki type and to present some basic problems of the fixed point and strict fixed point for them. Obtained results generalize, complement and extend classical results given by Ćirić [Lj.B. Ćirić, Fixed points for generalized multi-valued contractions, Mat. Vesnik 9 (24) (1972) 265–272] or Nadler [S.B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969) 475–488], as well as recent results given by Kikkawa and Suzuki [M. Kikkawa, T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal. 69 (2008) 2942–2949], Moţ and Petruşel [G. Moţ, A. Petruşel, Fixed point theory for a new type of contractive multivalued operators, Nonlinear Anal. 70 (2009) 3371–3377]. Applications to certain functional equations arising in dynamic programming are also considered.

RésuméLe but de cet article est dʼintroduire un nouveau type dʼopérateurs multivoques similaires ceux de Kikkawa–Suzuki type et de présenter certains problémes fondamentaux de la point fixe et stricte point fixe pour eux. Les résultats obtenus généraliser, compléter et étendre les résultats classiques donnés par Ćirić [Lj.B. Ćirić, Fixed points for generalized multi-valued contractions, Mat. Vesnik 9 (24) (1972) 265–272] ou Nadler [S.B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969) 475–488], comme ainsi que les résultats récents donné par Kikkawa et Suzuki [M. Kikkawa, T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal. 69 (2008) 2942–2949], Moţ et Petruşel [G. Moţ, A. Petruşel, Fixed point theory for a new type of contractive multivalued operators, Nonlinear Anal. 70 (2009) 3371–3377]. Applications à certaines équations fonctionnelles découlant de dynamique programmation sont également considérés.