Existence of fixed points involving the difference of two nonlinear operators



	Existence of fixed points involving the difference of two nonlinear operators


	Fixed Point Theory, Volume 25, No. 2, 2024, 677-684, June 15th, 2024 DOI: 10.24193/fpt-ro.2024.2.15 Authors: Claudio H. Morales Abstract: Let X be a uniformly smooth Banach space and let T, A be hemicontinuous operators defined on X with values in X. Suppose, in addition, that T is strongly pseudo-contractive (with constant k>0) while cI + A is accretive for 0 < c < 1-k. Then the operator T - A has a unique fixed point, which represents a significant extension of the main theorem in [12]. Some surjectivity results are also discussed, which are related to the main result. In particular, we begin with a surjectivity result for monotone operators defined on reflexive Banach spaces. Key Words and Phrases: Smooth Banach space, pseudo-contractive operator, fixed point, surjectivity. 2010 Mathematics Subject Classification: 47H10, 54H25. Published on-line: June 15th, 2024. Fulltext pdf Back to volume's table of contents