Fixed points for discontinuous quasi-monotone maps in sequence spaces

Kannan maps have inspired a branch of metric fixed point theory devoted to the extension of the classical Banach contraction principle. The study of these maps in modular vector spaces was attempted timidly and was not successful. In this work, we look at this problem in the variable exponent sequence spaces lp(·). We prove the modular version of most of the known facts about these maps in metric and Banach spaces. In particular, our results for Kannan nonexpansive maps in the modular sense were never attempted before.

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Fixed Points for Discontinuous Quasimonotone Maps in Sequence Spaces

Proceedings of the American Mathematical Society ◽

10.2307/2159253 ◽

1992 ◽

Vol 115 (2) ◽

pp. 361 ◽

Cited By ~ 2

Author(s):

Sabina Schmidt

Keyword(s):

Fixed Points ◽

Sequence Spaces ◽

Quasimonotone Maps

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Fixed points of contractive maps on dcpo's

Mathematical Structures in Computer Science ◽

10.1017/s0960129513000017 ◽

2013 ◽

Vol 24 (1) ◽

Cited By ~ 3

Author(s):

E. COLEBUNDERS ◽

S. DE WACHTER ◽

R. LOWEN

Keyword(s):

Fixed Point ◽

Fixed Points ◽

Fixed Point Theorems ◽

Scott Topology ◽

Study Approach ◽

Special Cases ◽

Monotone Maps ◽

Contractive Maps ◽

Approach Spaces

In this paper we study approach structures on dcpo's. A dcpo (X, ≤) will be endowed with several other structures: the Scott topology; an approach structure generated by a collection of weightable quasi metrics onX; and a collectionof weights corresponding to the quasi metrics. Understanding the interaction between these structures onXwill eventually lead to some fixed-point theorems for the morphisms in the category of approach spaces, which are called contractions. Existing fixed-point theorems on both monotone and non-monotone maps are obtained as special cases.

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Fixed Points of Kannan Maps in the Variable Exponent Sequence Spaces ℓp(·)

Mathematics ◽

10.3390/math8010076 ◽

2020 ◽

Vol 8 (1) ◽

pp. 76 ◽

Cited By ~ 1

Author(s):

Afrah Abdou ◽

Mohamed Khamsi

Keyword(s):

Fixed Point ◽

Fixed Points ◽

Banach Spaces ◽

Variable Exponent ◽

Fixed Point Theory ◽

Point Theory ◽

Sequence Spaces ◽

Vector Spaces ◽

Nonexpansive Maps ◽

Banach Contraction

Kannan maps have inspired a branch of metric fixed point theory devoted to the extension of the classical Banach contraction principle. The study of these maps in modular vector spaces was attempted timidly and was not successful. In this work, we look at this problem in the variable exponent sequence spaces ℓ p ( · ) . We prove the modular version of most of the known facts about these maps in metric and Banach spaces. In particular, our results for Kannan nonexpansive maps in the modular sense were never attempted before.

Download Full-text