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].

THE STUDY in fixed point theory has generally developed in three main directions: generalization of conditions which ensure existence, and, if possible, uniqueness, of fixed points; investigation of the character of the sequence of iterates (T”x)~~~, where T: X + X, X a complete metric space, is the map under consideration; study of the topoligical properties of the set of fixed points, wheneve...

We look for geometric structures which underlie both the 'classical' geometric and more modern 'order theoretic' conditions for a Banach space (dual space) to have the weak (weak*) fixed point property; that is, for every nonexpansive self-mapping of a nonempty weak (weak*) compact convex subset to have a fixed point.

Keywords: Upper and lower solutions p-Laplacian operator Fractional differential equation Integral boundary condition Eigenvalue a b s t r a c t In this paper, we are concerned with the eigenvalue problem of a class of singular p-Lapla-cian fractional differential equations involving the Riemann–Stieltjes integral boundary condition. The conditions for the existence of at least one positive sol...

We ask whether strictly causal components form well defined systems when arranged in feedback configurations. The standard interpretation for such configurations induces a fixed-point constraint on the function modelling the component involved. We define strictly causal functions formally, and show that the corresponding fixed-point problem does not always have a well defined solution. We exami...