Fixed point theorems for weakly contractive multivalued maps

Ekeland’s Variational Principle and Minimization Takahashi’s Theorem in Generalized Metric Spaces

“…Thus, h(w) ≤ h(u). Since ψ is nondecreasing, then ψ(h(v)) ≤ ψ(h(u)) by Definition 7 (1), (2) and (3), we get…”

“…After presentation of Ekeland Variational Principle (EVP) in 1972, it becomes clear that this principle is equivalent to Caristi fixed point theorem [1][2][3][4][5][6][7][8][9], Drop theorem [10,11], Flower Petal theorem [10,11] and Takahashi's nonconvex minimization theorem. Many scholars have studied EVP on complete convex space and on locally convex space.…”

Fixed point results for multivalued contractive maps

“…Since then, many authors have used the Hausdorff metric to obtain fixed point results for multivalued maps. For example, see [3][4][5][6], and references therein.…”

Maximal and minimal point theorems and Caristi's fixed point theorem

“…In the past decades, Caristi's fixed point theorem has been generalized and extended in several directions, and the proofs given for Caristi's result varied and used different techniques, we refer the readers to [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”