Then, by using a Himmelberg type fixed point theorem
in L[GAMMA]-spaces due to Park, they establish existence theorems of solutions for systems of generalized quasivariational inclusion problems, systems of variational equations, and systems of generalized quasiequilibrium problems in L[GAMMA]-spaces.
The Banach fixed point theorem
 (also known as a contraction mapping principle) is an important tool in nonlinear analysis.
De Blasi  introduced the concept of measure of weak noncompactness and proved the analogue of Sadovskiis fixed point theorem
for the weak topology (see also ).
They proved existence and uniqueness results for problem (3)-(4) by using the classical fixed point theorems
, such as Banach's fixed point theorem
, Boyd and Wong fixed point theorem
for nonlinear contractions, and Leray-Schauder nonlinear alternative.
It is worth mentioning that Caristi's fixed point theorem
is equivalent to the Ekeland variational principle .
In the paper, we introduce the concept of a new type of contraction maps, and we establish a new fixed point theorem
for such contraction maps in the setting of generalized metric spaces.
By exploiting Schauder's Fixed Point Theorem
the existence of periodic TWs is established.
Kirk, "A fixed point theorem
for mappings which do not increase distances," The American Mathematical Monthly, vol.
Mitrovic, "A fixed point theorem
for set-valued quasi-contractions in b-metric spaces," Fixed Point Theory and Applications, vol.
Nourouzi, "A generalization of Kannan and Chatterjea fixed point theorem
on complete b-metric spaces," Sahand Communications in Mathematical Analysis (SCMA), vol.
His topics include the canonical linear programming problem, basic feasible and basic optimal solutions, introduction to stochastic linear programming, Brouser's fixed point theorem
, and the four color problem.
Kirk, A fixed point theorem
for transformations whose iterates have uniform Lipschitz constant, Studia.