Convergence theorems for generalized contractions and applications

Abstract

The principal results in this article deal with the existence of fixed points of a new class of generalized F-contraction. In our approach, by visualizing some non-trivial examples we will obtain better geometrical interpretation. Our main results substantially improve the theory of F-contraction mappings and the related fixed point theorems. In section-4, application to graph theory is entrusted and proved results are endorsed by an example through graph. The presented new techniques give the possibility to justify the existence problems of the solutions for some class of integral equations. For the future aspects of our study, an open problem is suggested regarding discretized population balance model, whose solution may be derived from the established techniques.

A Solution of Fredholm Integral Inclusions via Suzuki-Type Fuzzy Contractions

“…Also, the generalization of Banach contraction principle has been done in many ways along with providing their applications in different fields. One of them is by generalizing the contraction condition, specially using nonlinear contractions, e.g., Suzuki-type contraction, F-contraction, and θ-contraction [10][11][12][13][14][15][16]. One of such generalizations, namely, ϕ-weak contraction was done by Alber and Guerre-Delabriere [17] in 1997 to prove fixed point result in the setting of Hilbert space, which was further utilized by Rhoades [18] in metric fixed point theory.…”

Double Controlled Partial Metric Type Spaces and Convergence Results

“…It is useful to establish the extensions of the contraction principle from metric spaces to b-metric spaces, and therefore the controlled metric type of spaces is useful to prove the existence and uniqueness of theorems for many forms of integral and differential equations. Some interesting applications can be found in the recent papers [4,[9][10][11][12][13][14][15]. It is always interesting to find novel applications dealing with engineering science and technology using fixed point technique.…”

On Some Common Fixed Point Results for Weakly Contraction Mappings with Application

“…Inspired by Czerwik's results, Hussain and Shah in [13] introduced the notion of a cone b-metric space, which means that it is a generalization of b-metric spaces and cone metric spaces; they considered topological properties of cone b -metric spaces and obtained some results on KKM mappings in the setting of cone b-metric spaces. Younis et al [14] studied the existence of fixed points of a new class of generalized F-contraction in partial b-metric space. In [15], some fixed point results for weakly contractive mappings in ordered partial metric space were obtained.…”