[PDF] Top 20 A generalization of Ekeland’s variational principle by using the τ distance with its applications

... Example . Let X = [, ∞ ] and d be the Euclidean metric on X. Consider the function p : X × X → R defined by p(x, y) = |y|, for all x, y ∈ X. The function p is a τ -distance (see Example .). Define the ... See full document

... By using such a w-distance concept, they improved some important theorems such as Caristi’s fixed point theorem, Ekeland’s variational principle and the nonconvex minimization ...of ... See full document

... In this paper, we prove a generalization of the strong Ekeland variational principle for a generalized distance (i.e., u-distance) on complete metric spaces. The result present ... See full document

... maximality principle is formulated and proved see Section 3. As applications, in cone uniform spaces with the families of generalized pseudodistances, the general variational principle of ... See full document

... Yao, “Some generalizations of Ekeland-type variational principle with applications to equilibrium problems and fixed point theory,” Nonlinear Analysis: Theory, Methods & Applications[r] ... See full document

... Remark 2.8 . Theorem 2.7 is a generalization of Caristi’s fixed point theorem [1]. The following theorem is a generalization of Ekeland’s ε -variational principle [3]. Theorem 2.9 . Let (X,d) ... See full document

... of τ -function 17 and a w-distance ...As applications, they derived the existence results for solutions of equilibrium problems and fixed point theorems for multivalued ...By using this ... See full document

... our variational principles with Caristi–Kirk type fixed point theorem for multi-valued maps, Takahashi’s minimization theorem, and some other related ...As applications of our results, we derive existence ... See full document

... contraction principle have appeared in literature. One of its most important extensions is known as Caristi’s fixed point ...Ekland variational principle 1, which is nowadays an important tool ... See full document

... a generalization of the Ekeland-type variational principle for vector valued functions in the setting of complete quasi-metric spaces with ω-distance was introduced by Ansari ... See full document

... ational principle and Noether theorem for both different physics systems and finite (infinite) freedom systems have neglected the key studies on the double extremum pro- cesses of the general extremum functional F ... See full document

... study of contraction mappings is easier than non-expansive mapping, so this type conversion has some importance in fixed point theory... I am thankful to Dr.[r] ... See full document

... In this paper, in order to study the dissipativity of nonlinear neutral functional differential equations, a generalization of the Halanay inequality is given. We apply this generalized Halanay inequality to an ... See full document

... Rayleigh’s principle of the least energy dissipation to general irreversible ...this variational principle gives us a very convenient framework for deriving many established equations which describe ... See full document

... variation principle of fuzzy mapping is proved and applied into the variation problem of fuzzy ...mappings. Its approximation and rules in sub-differential are ... See full document

... Yang, “On a generalization of the Hilbert type integral inequality and its applications,” Chinese Journal of Engineering Mathematics, vol.. Yang, “On a generalization of a Hilbert’s type[r] ... See full document

... Such a C is obviously a balanced set; for obtaining the remaining properties the same proof of Theorem 1 of 6 still works, with the unique following little change if F C for showing that cd / ∈ C when c > 1 and d ∈ D ... See full document

... Corollary . (Downing and Kirk []) Let X and Y be complete metric spaces, and T : X −→ X an arbitrary mapping. Suppose that there exist a closed mapping S : X −→ Y , a lower semicontinuous mapping ϕ : S( ... See full document

... to its in- completeness (or the (EF) model does not describes in “totus” the object “Un- iverse—(Space-Time)”), showing that the completeness is achieved if we include the expansion as a property of the Mass-Space ... See full document

... several applications like Skype that needs many access to various data on the phone; but there are a few applications like Wallpaper, Calendar, etc that require very few ...these applications used ... See full document