# K-metric and K-normed linear spaces: survey.

Collectanea Mathematica (1997)

- Volume: 48, Issue: 4-5-6, page 825-859
- ISSN: 0010-0757

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topZabrejko, P. P.. "K-metric and K-normed linear spaces: survey.." Collectanea Mathematica 48.4-5-6 (1997): 825-859. <http://eudml.org/doc/41051>.

@article{Zabrejko1997,

abstract = {We give a short survey on some fixed point theorems which are generalizations of the classical Banach-Caccioppoli principle of contractive mappings. All these results are gathered in three theorems about existence and uniqueness of fixed points for operators which act in K-metric or K-normed linear spaces and, in particular, in local convex spaces and scales of Banach spaces. Three fixed point theorems presented in this article cover numerous applications in numerical methods, theory of integral equations, some results on iterative methods for construction of periodic solution to ordinary differential equations, existence and uniqueness results on solvability for Cauchy and Goursat problems of Ovsjannikov-Treves-Nirenberg type and so on.},

author = {Zabrejko, P. P.},

journal = {Collectanea Mathematica},

keywords = {Espacios lineales topológicos; Espacios métricos; Espacios normados; Revisión bibliográfica; fixed point theorems; Banach-Caccioppoli principle; contractive mappings; existence and uniqueness; -metric or -normed linear spaces; scales of Banach spaces; periodic solution to ordinary differential equations; solvability of the Cauchy problem; Goursat problems},

language = {eng},

number = {4-5-6},

pages = {825-859},

title = {K-metric and K-normed linear spaces: survey.},

url = {http://eudml.org/doc/41051},

volume = {48},

year = {1997},

}

TY - JOUR

AU - Zabrejko, P. P.

TI - K-metric and K-normed linear spaces: survey.

JO - Collectanea Mathematica

PY - 1997

VL - 48

IS - 4-5-6

SP - 825

EP - 859

AB - We give a short survey on some fixed point theorems which are generalizations of the classical Banach-Caccioppoli principle of contractive mappings. All these results are gathered in three theorems about existence and uniqueness of fixed points for operators which act in K-metric or K-normed linear spaces and, in particular, in local convex spaces and scales of Banach spaces. Three fixed point theorems presented in this article cover numerous applications in numerical methods, theory of integral equations, some results on iterative methods for construction of periodic solution to ordinary differential equations, existence and uniqueness results on solvability for Cauchy and Goursat problems of Ovsjannikov-Treves-Nirenberg type and so on.

LA - eng

KW - Espacios lineales topológicos; Espacios métricos; Espacios normados; Revisión bibliográfica; fixed point theorems; Banach-Caccioppoli principle; contractive mappings; existence and uniqueness; -metric or -normed linear spaces; scales of Banach spaces; periodic solution to ordinary differential equations; solvability of the Cauchy problem; Goursat problems

UR - http://eudml.org/doc/41051

ER -

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