Caristi-type conditions in constraint minimisation of mappings in metric and partially ordered spaces

Sensitivity, stability, well-posedness (49K40) Monotone operators and generalizations (47H05) Set-valued and variational analysis (49J53) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Optimality conditions for problems in abstract spaces (49K27)

Cites Work

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Caristi's condition and existence of a minimum of a lower bounded function in a metric space. Applications to the theory of coincidence points
Extension of Caristi's fixed point theorem to vector valued metric spaces
Dynamics of pattern formation in lateral-inhibition type neural fields
Caristi's fixed point theorem and selections of set-valued contractions
Variational principles in nonlinear analysis and their generalization
Caristi-like condition and the existence of minima of mappings in partially ordered spaces
Generalized Caristi's fixed point theorems by Bae and others
Fixed points of asymptotic contractions
Equivalent conditions and the Meir-Keeler type theorems
Fixed-point theorem for asymptotic contractions of Meir--Keeler type in complete metric spaces
On a lemma of Bishop and Phelps
Spatially Structured Activity in Synaptically Coupled Neuronal Networks: I. Traveling Fronts and Pulses
Fixed Point Theorems for Mappings Satisfying Inwardness Conditions
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Evans Functions for Integral Neural Field Equations with Heaviside Firing Rate Function
Necessary Suboptimality and Optimality Conditions via Variational Principles
Eckland and Bishop-Phelps variational principles in partially ordered spaces
An induction theorem and Ekeland's variational principle in partial metric spaces with applications
Caristi-like condition. Existence of solutions to equations and minima of functions in metric spaces