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Coupled fixed point theorems under new coupled implicit relation in Hilbert spaces

Kim Kyung Soo

Demonstratio Mathematica

2022

Vol. 55, nr 1

81--89

The aim of this paper is to study existence and uniqueness of coupled fixed point for a family of self-mappings satisfying a new coupled implicit relation in a Hilbert space. We also prove well-posedness of a coupled fixed point problem.

Fixed point theorems on generalized metric spaces for mappings in a class of almost φ-contractions

Kikina L., Kikina K.

Demonstratio Mathematica

2015

Vol. 48, nr 3

440--451

In this paper, we obtain some new fixed point theorems in generalized metric spaces for maps satisfying an implicit relation. The obtained results unify, generalize, enrich, complement and extend a multitude of related fixed point theorems from metric spaces to generalized metric spaces.

A fixed point theorem in generalized metric spaces

Kikina L., Kikina K.

Demonstratio Mathematica

2013

Vol. 46, nr 1

181--190

A generalized metric space has been defined by Branciari as a metric space in which the triangle inequality is replaced by a more general inequality. Subsequently, some classical metric fixed point theorems have been transferred to such a space. In this paper, we continue in this direction and prove a version of Fisher’s fixed point theorem in generalized metric spaces.