The Schauder conjecture that every continuous single-valued map from a compact convex subset of a topological vector space into itself has a fixed point was stated in [12, Problem 54]. In a recent year, Cauty [2] gave a positive answer to this question by a very complicated approximation factorization. Very recently, Dobrowolski [3] established Cauty’s proof in a more accessible form by using t...

recently, zhang and song [q. zhang, y. song, fixed point theory forgeneralized $varphi$-weak contractions,appl. math. lett. 22(2009) 75-78] proved a common fixed point theorem for two mapssatisfying generalized $varphi$-weak contractions. in this paper, we prove a common fixed point theorem fora family of compatible maps. in fact, a new generalization of zhangand song's theorem is given.

In the present research, we study boundary value problems for fractional integro-differential equations and inclusions involving Hilfer derivative. Existence uniqueness results are obtained by using classical fixed point theorems of Banach, Krasnosel’skiĭ, Leray–Schauder in single-valued case, while Martelli’s theorem, a nonlinear alternative multivalued maps, Covitz–Nadler theorem used inclusi...

Recently, Zhang and Song [Q. Zhang, Y. Song, Fixed point theory forgeneralized $varphi$-weak contractions,Appl. Math. Lett. 22(2009) 75-78] proved a common fixed point theorem for two mapssatisfying generalized $varphi$-weak contractions. In this paper, we prove a common fixed point theorem fora family of compatible maps. In fact, a new generalization of Zhangand Song's theorem is given.

In this paper, we consider a second-order m-point impulsive boundary value problem. By applying the upper and lower solutions method Schauder?s fixed point theorem, obtain existence of at least one positive solution. We also give an example to illustrate our main result.

This paper is devoted to investigating the existence of solutions for fractional differential equation and inclusion order ??(2,3] with affine periodic boundary value conditions. Applying Leray–Schauder fixed point theorem, established. Furthermore, inclusion, we consider two cases: (i) set-valued function has convex (ii) nonconvex value. The main tools our research are alternative Covita Nadle...

Under suitable assumptions we prove, via the Leray-Schauder fixed point theorem, the existence of a solution for quasilinear elliptic boundary value problem in C(Ω̄) ∩ W (Ω), q > N which satisfies in addition the condition, (1+ | x |) 1 2u ∈ C(Ω̄).