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Fixed point theorems for integral type contraction condition in 2-metric space

Barman Dinanath, Sarkar Krishnadhan, Tiwary Kalishankar

Fasciculi Mathematici

2021

nr 65

17--37

In this paper we have introduced a new type of contraction mapping Fα-contraction which is the generalization of Fα-contraction and proved some common fixed point theorems using integral type contraction condition.

Some fixed point theorems for almost (GF, δb)-contractions and application

Nashine H. K., Agarwal R. P., Shukla S., Gupta A.

Fasciculi Mathematici

2017

Nr 58

123--143

We propose a new notion of multi-valued almost (GF, δb)-contractions involving rational terms under δ-distance on b-metric spaces and give its relevance to fixed point results in orbitally complete b-metric spaces. An ordered version of our main result is also proved with some weaker contractive conditions. Some examples are given to show the usability of the results proved herein. Moreover, application of our result to the nonlinear integral equation is given.

Fixed points of F-weak contractions on complete metric spaces

Wardowski D., Dung N.V.

Demonstratio Mathematica

2014

Vol. 47, nr 1

147--155

In this paper, we introduce the notion of an F-weak contraction and prove a fixed point theorem for F-weak contractions. Examples are given to show that our result is a proper extension of some results known in the literature.