Schauder fixed-point theorem in semilinear spaces and its application to fractional differential equations with uncertainty

Application of Schauder fixed point theorem to a coupled system of differential equations of fractional order

In this paper, by using Schauder fixed point theorem, we study the existence of at least one positive solution to a coupled system of fractional boundary value problems given by { −D1 0+ y1(t) = λ1a1(t)f(t, y1(t), y2(t)) + e1(t), −D2 0+ y2(t) = λ2a2(t)g(t, y1(t), y2(t)) + e2(t), where ν1, ν2 ∈ (n− 1, n] for n > 3 and n ∈ N , subject to the boundary conditions y 1 (0) = 0 = y (i) 2 (0), for 0 ≤ ...

A Contraction Fixed Point Theorem in Partially Ordered Metric Spaces and Application to Fractional Differential Equations

and Applied Analysis 3 Besides, if for any x, y ∈ M, there exists z ∈ M which is comparable to x and y, 2.4 then f has a unique fixed point. Proof. We first show that f has a fixed point. Since x0 f x0 and f is an increasing function, we obtain by induction that x0 f x0 f2 x0 f3 x0 · · · f x0 · · · . 2.5 Put xn 1 f x0 , n 1, 2, . . . For each integer n ≥ 1, from 2.5 , we have xn xn 1, then by 2...

Schauder Fixed Point Theorem in Spaces with Global Nonpositive Curvature

A Fixed Point Theorem and Its Application to Integral Equations in Modular Function Spaces

In this paper we present a fixed point theorem of Banach type in modular space. We give an application of this result to a nonlinear integral equation in Musielak-Orlicz space. 0. Introduction It is well known that one of the standard proofs of Banach’s fixed point theorem is based on Cantor’s theorem in complete metric spaces [3, 4]. To this end, using some convenient constants in the contract...

Transversal spaces and common fixed point Theorem

In this paper we formulate and prove some xed and common xed pointTheorems for self-mappings dened on complete lower Transversal functionalprobabilistic spaces.