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.

Abstract: In this work, by employing the Leggett-Williams fixed point theorem, we study the existence of at least three positive solutions of boundary value problems for system of third-order ordinary differential equations with (p,q)-Laplacian  (φp(u ′′(t)))′ + a1(t)f1(t, u(t), v(t)) = 0 0 ≤ t ≤ 1, (φq(v ′′(t)))′ + a2(t)f2(t, u(t), v(t)) = 0 0 ≤ t ≤ 1, α1u(0)− β1u(0) = μ11u(ξ1), γ1u(1) +...

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...

in the present paper, a partial order on a non- archimedean fuzzymetric space under the  lukasiewicz t-norm is introduced and fixed point theoremsfor single and multivalued mappings are proved.

the main purpose of this paper is to establish some new results onthe superstability and stability via a fixed point approach forthe pexiderized exponential equation, i.e.,$$|f(x+y)-g(x)h(y)|leq psi(x,y),$$where $f$, $g$ and $h$ are three functions from an arbitrarycommutative semigroup $s$ to an arbitrary unitary complex banachalgebra and also $psi: s^{2}rightarrow [0,infty)$ is afunction. fur...

in this paper, vector ultrametric spaces are introduced and a fixed point theorem is given forcorrespondences. our main result generalizes a known theorem in ordinary ultrametric spaces.

This paper is concerned with a 2nth-order p-Laplacian difference equation. By using the critical point method, we establish various sets of sufficient conditions for the nonexistence and existence of solutions for Neumann boundary value problem and give some new results. Results obtained successfully generalize and complement the existing ones.