Convergence of three-step iterations for Ciric-quasi contractive operator in CAT(0) spaces

In this paper, we study three-step iteration process for Ciric-quasi contractive operator and establish strong convergence theorems for above mentioned operator and schemes in the setting of CAT(0) spaces. Our result extends and generalizes some previous work from the existing literature (see, e.g., [4, 30] and some others).

Existence and Global Attractivity of Positive Periodic Solutions for The Neutral Multidelay Logarithmic Population Model with Impulse

Suffiicient and realistic conditions are established in this paper for the existence and global attractivity of a positive periodic solution to the neutral multidelay logarithmic population model with impulse by using the theory of abstract continuous theorem of k-set contractive operator and some inequality techniques. The results improve and generalize the known ones in Li 1999, Lu and Ge 2004, Y. Luo and Z. G. Luo 2010, and Wang et al. 2009. As an application, we also give an example to illustrate the feasibility of our main results.

Existence of Periodic Solutions for Shunting Inhibitory Cellular Neural Networks with Neutral Delays

This paper considers the existence of periodic solutions for shunting inhibitory cellular neural networks (SICNNs) with neutral delays. By applying the theory of abstract continuation theorem ofk-set contractive operator and some analysis technique, a new result on the existence of periodic solutions is obtained.

Contractive analogs

This chapter deals with contractive completions of partial operator matrices. Since the norm of a submatrix is always less or equal to the norm of the matrix itself, every partial matrix which admits a contractive completion has to be partially contractive (or a partial contraction), that is, all its fully specified submatrices are contractions. The discussions cover contractive operator-matrix completions; linearly constrained completion problems; the operator-valued Nehari and Carathéodory problems; Nehari's problem in two variables; Nehari and Carathéodory problems for functions on compact groups; the Nevanlinna–Pick problem; the operator Corona problem; joint operator/Hilbert–Schmidt norm control extensions; an L1 extension problem for polynomials; superoptimal completions and approximations of analytic functions; and model matching. Exercises and notes are provided at the end of the chapter.