Dynamic processes and fixed points of set-valued nonlinear contractions in cone metric spaces

Fixed point theorems for multivalued maps in cone metric spaces

“…Thus, there exists v n Tu such that (2) The authors [26,28]obtained fixed point theorems for multivalued maps T defined on cone metric spaces (X, d) under assumption that the function I(x) = inf x Tx ||d(x, y)|| is lower semicontinuous, and the author [27]obtained a fixed point theorem for multivalued maps T under assumptions that the function I(x), x X is lower semicontinuous and a dynamic process is given.…”

“…(3) In [26][27][28], the authors do not use the concept of the Hausdorff metric on cone metric spaces, and their results cannot be applied directly to obtain the following corollaries 2.2-2.5.…”

Fixed Points and Variational Principle With Applications to Equilibrium Problems on Cone Metric Spaces

“…Also, the authors [7,23,32] proved fixed point results under assumption that the cone is regular. And the authors [4,9,17,18,19,21,20,27,28] do not use the notion of normality or regularity to obtain their results on cone metric spaces.…”

On set-valued contractions of Nadler type in tυs-G-cone metric spaces

“…However, authors like Jankovic' et al [3], Rezapour and Hamlbarani [4] studied the existence of common fixed points of a pair of self and nonself mappings satisfying a contractive type condition in the situation in which the cone does not need to be normal. Many authors studied this subject and many results on fixed point theory are proved (see e.g., [4][5][6][7][8][9][10][11][12][13][14][15]). …”