Further, we introduce our earlier related works as a history of our Metatheorem.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:Certain maximum principles can be reformulated to various types of fixed point theorems and conversely, based on Metatheorem due to ourselves.
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Temel Bulgular & Veri:Such principles are Zorn's lemma, Banach contraction principle, Nadler's fixed point theorem, Brézis-Browder principle, Caristi's fixed point theorem, Ekeland's variational principle, Takahashi's nonconvex minimization theorem, some others, and their variants, generalizations, or equivalent formulations.
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Sonuç & Katkı:Further, we introduce our earlier related works as a history of our Metatheorem.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Banach · Nadler · Zorn
Abstract
Certain maximum principles can be reformulated to various types of fixed point theorems and conversely, based on Metatheorem due to ourselves. Such principles are Zorn's lemma, Banach contraction principle, Nadler's fixed point theorem, Brézis-Browder principle, Caristi's fixed point theorem, Ekeland's variational principle, Takahashi's nonconvex minimization theorem, some others, and their variants, generalizations, or equivalent formulations. Consequently, we have many new theorems equivalent to known results on fixed point, common fixed point, stationary point, common stationary point, and others. We show that such points are all maximal elements of certain ordered sets. Further, we introduce our earlier related works as a history of our Metatheorem.
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S. Park, On extensions of the Caristi-Kirk fixed point theorem, J. Korean Math. Soc. 19 (1983), 143-151
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S. Park, Remarks on fixed point theorems of Downing and Kirk for set-valued mapping in metric and Banach spaces, Bull. Korean Math. Soc. 21 (1984), 55-60
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S. Park, On fixed points of set-valued directional contractions, Internat. J. Math. & Math. Sci. 8 (1985), 663-667
S. Park, Some applications of Ekeland's variational principle to fixed point theory, in Approximation Theory and Applications (S.P. Singh, ed.), Pitman Res. Notes Math. 133 (1985), 159-172