On Fixed Point Results in Controlled Metric Spaces

Abstract

In this article, we introduce Reich type contractions and ( α , F )-contractions in the class of controlled metric spaces and establish some new related fixed point theorems. Our results are generalizations of some known results of literature. Some examples and certain consequences are given to illustrate significance of presented results.

Fixed Points of E-Contraction in Controlled Metric Spaces

“…This paper's main objective is to propose a fixed-point theorem for E-contractions in the context of complete controlled metric spaces. Our finding broadens and generalises a few established findings in the literature [24][25][26][27][28][29][30][31][32]. We also provide examples to highlight the applicability of the findings made in E-contractive circumstances.…”

Reich-Type and (α, F)-Contractions in Partially Ordered Double-Controlled Metric-Type Spaces with Applications to Non-Linear Fractional Differential Equations and Monotonic Iterative Method

“…In addition, he established some interesting examples to show the authenticity of the established results. Ahmad et al [17] introduced Reich-type contractions and (α, F)-contractions on a controlled metric-type space and generalized some known results from the literature. In 2012, the structure of the F-contraction was presented by Wardowski [18] and established new remarkable results in the context of complete metric spaces and established a more generalized form of the Banach contraction principle.…”

Fixed Point Results in Controlled Metric Spaces with Applications

“…Ahmad [6] established a Reich type fixed-point theorem in the setting of controlled metric space as follows. Theorem 3.…”

“…Later on, Abuloha et al [7], Alamgir et al [8], Abdeljawad et al [9], Lateef [10], Hussain [11], Mlaiki et al [12], Shatanawi et al [13], Sezen et al [14] and Tasneem et al [15] studied controlled metric spaces and established different fixed-point results for self and multivalued mappings. For more details, in this direction, we refer the readers to [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”