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Existence of Exponentialp-Stability Nonconstant Equilibrium of Markovian Jumping Nonlinear Diffusion Equations via Ekeland Variational Principle

Ruofeng Rao, Shouming Zhong
2015 Advances in Mathematical Physics  
As far as we know, it is the first time to apply Ekeland variational principle to obtain the existence of exponential stability equilibrium ofp-Laplacian dynamic system so that some methods used in this  ...  In addition, the obtained existence criterion is only involved in the activation functions so that the criterion is simpler and easier than other existence criteria to be verified in practical application  ...  Advances in Mathematical Physics  ... 
doi:10.1155/2015/812150 fatcat:pwsky4kg5ncjznzdoyjeu6p6am

Caristi Type Coincidence Point Theorem in Topological Spaces

Jiang Zhu, Lei Wei, Cheng-Cheng Zhu
2013 Journal of Applied Mathematics  
uniform spaces withq-distance, generating spaces of quasimetric family, and fuzzy metric spaces.  ...  A generalized Caristi type coincidence point theorem and its equivalences in the setting of topological spaces by using a kind of nonmetric type function are obtained.  ...  valued, Caristi type fixed point theorem for single-valued map, Ekeland type variational principles and its equivalences in the setting of topological spaces are obtained.  ... 
doi:10.1155/2013/902692 fatcat:swslihawb5hvjiajhm7gdnzenm

Page 6876 of Mathematical Reviews Vol. , Issue 99j [page]

1999 Mathematical Reviews  
In order to extend Ekeland’s variational principle to the case of fuzzy metric spaces, the authors introduce fuzzy bounded subsets in fuzzy metric spaces.  ...  principle in fuzzy and probabilistic metric spaces.  ... 

Page 66 of Mathematical Reviews Vol. , Issue 2004a [page]

2004 Mathematical Reviews  
The author derives an Ekeland-type variational principle for set- valued mappings taking into account their graphs on the basis of a scalarization technique.  ...  The author presents some equivalent formulations of Ekeland’s variational principle in F-type topological spaces obtained by using a family of weak quasi-metrics.  ... 

Page 7874 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
He, Yong Fu |He, Yong Fu*] (PRC-LAN; Lanzhou) A variational principle on locally compact metric spaces.  ...  The authors prove a result which is similar to (and deeper than) Ekeland’s variational principle [I. Ekeland, J. Math. Anal.  ... 

Page 1160 of Mathematical Reviews Vol. , Issue 86c [page]

1986 Mathematical Reviews  
Ekeland on the variational principle for approximate solutions of minimization problems. S. Swaminathan (Halifax, N.S.) Rao, I. H. N. (6-ANDH); 86c:54046 Rao, K. P.  ...  Park, Sehie (KR-SNU) 86c:54045 Remarks on fixed point theorems of Downing and Kirk for set-valued mappings in metric and Banach spaces. Bull. Korean Math. Soc. 21 (1984), no. 2, 55-60.  ... 

Caristi's fixed point theorem and its equivalences in fuzzy metric spaces

Naser Abbasi, Hamid Mottaghi Golshan
2017 Kybernetika (Praha)  
INTRODUCTION Since Ekeland [10] in 1972 (see also [11, 12] ), the variational principle in the setting of complete metric spaces, now known as Ekeland's variational principle and its equivalent formulations  ...  (Ekeland's variational principle) Let (X, M, * ) be a complete GV space endowed with a continuous and Archimedean t-norm * and let φ be a nontrivial u.s.c. fuzzy set of X.  ... 
doi:10.14736/kyb-2016-6-0929 fatcat:4ixkxbv3w5dappxj6uchpzt4am

Page 5115 of Mathematical Reviews Vol. , Issue 98H [page]

1998 Mathematical Reviews  
Ekeland’s variational principle in fuzzy metric spaces.  ...  The last chapter of the book contains generalizations of the well-known Caristi fixed point theorem and the Ekeland variational principle in PM spaces.”  ... 

Page 1118 of Mathematical Reviews Vol. , Issue 2001B [page]

2001 Mathematical Reviews  
In the fi- nal Section 7, the author briefly reviews some recent results on nonsmooth analysis, especially fuzzy sum rules and mean value theorems.  ...  C Lionel Thibault (F-MONT2; Montpellier) 2001b:49026 49J53 47H10 47530 S4H25 Kang, Byung Gai (KR-SSWU,; Seoul); Kim, Jeong-Heon Nonmetric versions of the Ekeland type variational principles.  ... 

Extremality, Stationarity and Generalized Separation of Collections of Sets [article]

Hoa T. Bui, Alexander Y. Kruger
2018 arXiv   pre-print
The core arguments used in various proofs of the extremal principle and its extensions as well as in primal and dual characterizations of approximate stationarity and transversality of collections of sets  ...  For that, we examine and clarify quantitative relationships between the parameters involved in the respective definitions and statements.  ...  Ekeland Variational Principle (EVP) Suppose X is a complete metric space, f : X → R ∞ is lower semicontinuous,x ∈ X, and ε > 0.  ... 
arXiv:1808.05740v3 fatcat:njs76t2xfnh6tmf7uxl2bps7lq

Extremality, Stationarity and Generalized Separation of Collections of Sets

Hoa T. Bui, Alexander Y. Kruger
2018 Journal of Optimization Theory and Applications  
The core arguments used in various proofs of the extremal principle and its extensions as well as in primal and dual characterizations of approximate stationarity and transversality of collections of sets  ...  For that, we examine and clarify quantitative relationships between the parameters involved in the respective definitions and statements.  ...  Ekeland Variational Principle (EVP) Suppose X is a complete metric space, f : X → R ∞ is lower semicontinuous,x ∈ X, and ε > 0.  ... 
doi:10.1007/s10957-018-01458-8 fatcat:htaozol6d5gqlcbqzcpxoo73k4

A note on implicit multifunction theorems

T. T. A. Nghia
2012 Optimization Letters  
The paper is mainly devoted to the study of implicit multifunction theorems in terms of Fréchet coderivative in Asplund spaces.  ...  It sharpens the well-known implicit multifunction theorem of Ledyaev and Zhu (Set Valued Anal., 7, 209-238, 1999) as well as many recent publications about this significant area.  ...  Our approach seems much simpler since we only use the Ekeland variational principle and the fuzzy sum rule.  ... 
doi:10.1007/s11590-012-0580-7 fatcat:32rgiprgvnaj7fukh5w5pl3hn4

Page 7722 of Mathematical Reviews Vol. , Issue 99k [page]

1999 Mathematical Reviews  
99k:54005 quasi-metrics, we prove a Takahashi-type minimization theorem, a generalized Ekeland variational principle and a general Caristi- type fixed point theorem for set-valued maps in complete generat  ...  From our results in complete generat- ing spaces of quasi-metric family, we obtain the corresponding theorems for set-valued maps in complete fuzzy metric spaces.”  ... 

On fuzzy order relations

Ismat Beg
2012 Journal of Nonlinear Science and its Applications  
In this review article we present results regarding the fuzzy order relations.The concept of fuzzy order was introduced by generalizing the notion of reflexivity, antisymmetric and transitivity.  ...  Next, we prove Ekeland's variational principle in fuzzy metric spaces. Theorem 6.7.[Ekeland's variational principle].  ...  Afterwards fuzzy analogue of fixed point theorems and Ekeland's variational principle in fuzzy metric spaces were studied by Kaleva [61] , Hadzic [51] , Fang [48] , He [53] , Jung, Cho, Kang and Chang  ... 
doi:10.22436/jnsa.005.05.06 fatcat:sghektxqq5f7jpy2raqtsjo56u

Calmness of efficient solution maps in parametric vector optimization

T. D. Chuong, A. Y. Kruger, J.-C. Yao
2011 Journal of Global Optimization  
Utilizing the advanced tools of modern variational analysis and generalized differentiation, we study the calmness of the efficient solution map.  ...  More explicitly, new sufficient conditions in terms of the Fréchet and limiting coderivatives of parametric multifunctions for this efficient solution map to have the calmness at a given point in its graph  ...  In what follows we also use the Ekeland variational principle [10] . Lemma 2.2 (Ekeland Variational Principle).  ... 
doi:10.1007/s10898-011-9651-z fatcat:zlchpgwvpvgjpagv4xas3b4p4a
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