This paper discusses the existence of solutions to antiperiodic boundary value problem for nonlinear impulsive fractional differential equations. By using Banach fixed point theorem, Schaefer fixed point theorem, and nonlinear alternative of Leray-Schauder type theorem, some existence results of solutions are obtained. An example is given to illustrate the main result.

The theory of fixed point is a very extensive field, which has various applications. The present paper deals with some developments of Meir-Keeler type fixed point theorem as its remarkable generalizations under several contractive definitions in metric space.

Very recently, Ma et al. (Fixed Point Theory Appl. 2014:206, 2014) introduced C∗-algebra-valued metric spaces as a new concept. Also, Ma and Jiang (Fixed Point Theory Appl. 2015:222, 2015), generalizing this concept, introduced C∗-algebra-valued b-metric spaces. In both frameworks, these and other authors proved some fixed point results. We show in this paper that all these results (as well as ...

*Correspondence: [email protected] School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P.R. China Abstract In this paper, we establish some sufficient conditions for the existence of solutions to two classes of boundary value problems for fractional differential equations with nonlocal boundary conditions. Our goal is to establish some criteria of existence for the bound...

A common fixed point result for weakly increasing mappings satisfying generalized contractive type of Zhang in ordered metric spaces are derived.

In this article, by using Schaefer fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for a class of impulsive integro-differential equations with nonlocal conditions involving the Caputo fractional derivative.

In this paper, we discuss a class of integrodifferential equations with nonlocal conditions via a fractional derivative of the type: D t x(t) = Ax(t) + t Z 0 B(t − s)x(s)ds + tf (t, x(t)) , t ∈ [0, T ], n ∈ Z, q ∈ (0, 1], x(0) = g(x) + x0. Some sufficient conditions for the existence of mild solutions for the above system are given. The main tools are the resolvent operators and fixed point the...

In this paper, we prove common fixed point theorems for hybrid pairs of mappings satisfying an implicit relation in 2-metric spaces by using a new commutativity condition i.e. weak commutativity of type (KB). We also prove common fixed point theorem, of Gregus type for hybrid pairs of maps by using weak commutativity of type (KB) in 2-metric spaces. We extend, improve and generalize many known ...

The main purpose of this paper is to study the existence of a fixed points in fuzzy n-normed spaces. we proved our main results, a fixed point theorem for a self mapping and a common fixed point theorem for a pair of weakly compatible mappings on fuzzy n-normed spaces. Also we gave some remarks on fuzzy n-normed spaces.

In this paper, we prove some fixed point theorems for weakly compatible mappings by improving the conditions of Som [8].