The purpose of this work is to investigate the existence of fixed points of some mappings in fixed point theory by combining some important concepts which are F-weak contractions, multivalued mappings, integral transformations and α-admissible mappings. In fixed point theory, it is important to find fixed points of some classess under F- or F-weak contractions. Also multivalued mappings is the ...

the main purpose of this paper is to obtain sufficient conditions for existence of points of coincidence and common fixed points for three self mappings in $b$-metric spaces. next, we obtain cone $b$-metric version of these results by using a scalarization function. our results extend and generalize several well known comparable results in the existing literature.

The Lefschetz fixed point theorem follows easily from the identification of the Lefschetz number with the fixed point index. This identification is a consequence of the functoriality of the trace in symmetric monoidal categories. There are refinements of the Lefschetz number and the fixed point index that give a converse to the Lefschetz fixed point theorem. An important part of this theorem is...

In this paper, we investigate nonlinear fractional differential equations of arbitrary order with advanced arguments    D 0+u(t) + a(t)f(u(θ(t))) = 0, 0 < t < 1, n− 1 < α ≤ n, u(i)(0) = 0, i = 0, 1, 2, · · · , n− 2, [D 0+ u(t)]t=1 = 0, 1 ≤ β ≤ n− 2, where n > 3 (n ∈ N), D 0+ is the standard Riemann-Liouville fractional derivative of order α, f : [0,∞) → [0,∞), a : [0, 1] → (0,∞) and θ : (0, ...

The Brouwer Fixed Point Theorem states that any continuous mapping from a closed ball in Euclidean space to itself has at least one fixed point. This theorem has a wide variety of applications in areas such as differential equations, economics, and game theory. Although this is fundamentally an analytic and topological statement, there exists an elegant combinatorial proof using Sperner’s Lemma...

&lt;abstract&gt;&lt;p&gt;The goal of this paper is to present a new class contraction mappings, so-called $ \eta _{\theta }^{\ell } $-contractions. Also, in the context partially ordered metric spaces, some coupled fixed-point results for $-contraction mappings are introduced. Furthermore, support our results, two examples provided. Finally, theoretical applied obtain existence solutions fracti...