New Results in Controlled Metric Type Spaces

Abstract

In this paper, a new class of functions denoted by Ψ ν is introduced which we use to prove new interesting fixed point results in controlled metric type spaces. Also, we present examples to illustrate our work.

Fixed Point Results in Controlled Metric Spaces with Applications

“…Letting n → ∞ and using (7), we obtain a contradiction to τ(µ * , V µ * ) > 0. Thus, τ(µ * , V µ * ) = 0.…”

“…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].…”

Fixed-Point Approaches for Multi-Valued Contraction Mappings in a Novel Space With an Application

“…Definition 2.2. [38] Assume that ∅ is a given set and S : 3 → R + (where 3 = × × ) is a function fulfilling the hypotheses below for all θ, ϑ, ρ, ν ∈ ,…”

Common Fixed Point Results on a Double-Controlled Metric Space for Generalized Rational-Type Contractions with Application

“…Mustafa et al [12] used the idea of extended b-MS and presented the notion of extended rectangular b-MS. Lateef [13] proved the fixed point theorem for Kannan-type contraction mapping in the context of CMSs. Abuloha et al [14] derived several fixed point results for CMSs by utilizing the class of functions denoted by ψ γ . For more related results in the setting of controlled-type MSs, see [15,16].…”