Common fixed points via implicit contractions on b-metric-like spaces

Abstract

In this paper, we introduce some generalized nonlinear contractions via implicit functions and α-admissible pair of mappings. We also provide some common fixed point results for above contractions in the class of b-metric-like spaces. We will derive some consequences and corollaries from our obtained results. Some illustrated examples are presented to make effective the concepts and results.

Some New Observations on Geraghty and Ćirić Type Results in b-Metric Spaces

“…However, our approach does not require this lemma and the proof is much shorter. Namely, we consider the following: Ω (µ, τ) ψ (s ε d (Tµ, Tτ)) ≤ β (E (µ, τ)) ψ (E (µ, τ)) + Lφ (N (µ, τ)) , where ε > 1, instead Equation (15). On the other hand, d (µ n+1 , µ n ) ≤ 1 s ε d (µ n , µ n−1 ) , n ≥ 1.…”

Fixed Point Results for Multi-Valued Contractions in b−Metric Spaces and an Application

“…The Banach contraction principle is considered to be one of the most useful tools in fixed point theory. It has been extended or generalized in different directions and many (common) fixed point theorems have been provided (see References [1][2][3][4][5][6][7][8][9][10][11][12][13]). The theory of fixed points for multi-valued mappings has been developed after the famous paper of Nadler [14].…”

Some Results on (s − q)-Graphic Contraction Mappings in b-Metric-Like Spaces

“…It is clear that each metric-like space, i.e., each partial b-metric space, is a b-metric-like space, while the converse is not true. For more such examples and details see [1,2,[5][6][7][15][16][17][18][19][20][21][22][23][24][25][26][27]. Moreover, for various metrics in the context of the complex domain see [28,29].…”