A generalized non-smooth fixed point theorem on finite dimensional ordered Banach spaces via Clarke generalized Jacobian
Subject Areas : Statistics
Razieh Zohari
1
(
Ph.D. Student / Department of Mathematics, Faculty of Science, Science and Research Branch, Islamic Azad University, Tehran; Iran.
)
Mohammadreza Mardanbeigi
2
(
Assistant Professor / Department of Mathematics, Faculty of Science, Science and Research Branch, Islamic Azad University, Tehran, Iran.
)
Keywords: فضای باناخ مرتب, ژاکوبین تعمیم یافته کلارک, نقطه ثابت,
Abstract :
Ordered Banach spaces are very significant class of vector spaces which are studied widely in theory and applications of mathematics. On the other hand, an important theory in mathematical analysis is fixed point theory. This theory and its applications in ordered Banach spaces have been considered by many researchers. Lakshmikantham have proved some fixed point theorems in ordered Banach space X for a Fréchet differentiable automorphism on X. Mouhadjer and Benahmad obtained some generalizations of Lakshmikantham’s fixed point theorems. They introduced a monoton Newton-like method, by using Lakshmikantham’s fixed point theorems. Recently, a non-smooth version of Lakshmikantham’s theorem in finite dimentional ordered Banach spaces.has been obtained by authores. Also an application of the obtained results in the Coulomb friction problem has been presented. In this paper, we present a non-smooth version of Mouhadjer and Benahmad’s results. We prove some fixed point theorems for Lipschitzian mappings on finite Banach spaces which are not necessary Fréchet differentiable. Our main tool is Clarke generalized Jacobian
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