Common Fixed Point Results for Six Mappings via Integral Contractions with Applications

Zada, Mian Bahadur; Sarwar, Mohammed; Mehmood, Nayyar

doi:10.1155/2016/7480469

Cited by 2 publications

(1 citation statement)

References 18 publications

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“…Kanwal et al [7], introduced a new type of contractive condition for contractive mappings to prove the fixed-point theorems in the settings of b-metric space. More articles related to this study are in [8][9][10][11][12][13][14][15] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Exploring Integral ϝ-Contractions with Applications to Integral Equations and Fractional BVPs

Nisar,

Mehmood,

Azam

et al. 2023

Fractal Fract

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In this article, two types of contractive conditions are introduced, namely extended integral Ϝ-contraction and (ϰ,Ω-Ϝ)-contraction. For the case of two mappings and their coincidence point theorems, a variant of (ϰ,Ω-Ϝ)-contraction has been introduced, which is called (ϰ,Γ1,2,Ω-Ϝ)-contraction. In the end, the applications of an extended integral Ϝ-contraction and (ϰ,Ω-Ϝ)-contraction are given by providing an existence result in the solution of a fractional order multi-point boundary value problem involving the Riemann–Liouville fractional derivative. An interesting existence result for the solution of the nonlinear Fredholm integral equation of the second kind using the (ϰ,Γ1,2,Ω-Ϝ)-contraction has been proven. Herein, an example is established that explains how the Picard–Jungck sequence converges to the solution of the nonlinear integral equation. Examples are given for almost all the main results and some graphs are plotted where required.

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