Best approximations theorem for a couple in cone Banach space

DOI10.1155/2010/784578zbMath1204.47067OpenAlexW2167831875WikidataQ59253748 ScholiaQ59253748MaRDI QIDQ1958055

Erdal Karapınar, Duran Türkoǧlu

Publication date: 28 September 2010

Published in: Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2010/784578

zbMATH Keywords

best approximation theoremcoupled fixed pointscone Banach spaces

Mathematics Subject Classification ID

Normed linear spaces and Banach spaces; Banach lattices (46B99) Fixed-point theorems (47H10) Fixed-point and coincidence theorems (topological aspects) (54H25) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Other ``topological linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than (mathbb{R}), etc.) (46A19)

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Some fixed point results on generalized metric spaces ⋮ Common new fixed point results on b-cone Banach spaces over Banach algebras ⋮ Common fixed point theorems on quasi-cone metric space over a divisible Banach algebra ⋮ A fixed point theorem and an application for the Cauchy problem in the scale of Banach spaces ⋮ Mizoguchi-Takahashi-type theorems in tvs-cone metric spaces ⋮ Fixed point theorems for multivalued contractive mappings and multivalued Caristi type mappings in cone metric spaces ⋮ Coupled fixed-point results for \(T\)-contractions on cone metric spaces with applications ⋮ Coupled coincidence point and common coupled fixed point theorems lacking the mixed monotone property ⋮ A note on Stone's, Baire's, Ky Fan's and Dugundji's theorem in tvs-cone metric spaces ⋮ On cone metric spaces: a survey ⋮ Common fixed points of weak contractions in cone metric spaces ⋮ Some Coupled fixed point theorems in partially ordered A_b-metric space ⋮ Extended \(N_b\)-cone metric spaces over Banach algebra with an application ⋮ A note on the paper "A fixed point theorems in Sb-metric spaces"

Cites Work

• Coupled fixed point theorems for nonlinear contractions in cone metric spaces
• A common fixed point theorem for a class of mappings
• Cone metric spaces and fixed point theorems of contractive mappings
• Some notes on the paper ``Cone metric spaces and fixed point theorems of contractive mappings
• A coupled best approximations theorem in normed spaces
• Fixed point theorem for two non-self mappings in cone metric spaces
• Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces
• \(\varphi\)-pairs and common fixed points in cone metric spaces
• KKM mappings in cone metric spaces and some fixed point theorems
• A common fixed point theorem in abstract spaces
• Cone metric spaces and fixed point theorems in diametrically contractive mappings
• Quasicone metric spaces and generalizations of Caristi Kirk's theorem
• Fixed point theorems in cone Banach spaces
• Fixed point theorems in partially ordered metric spaces and applications
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