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Probabilistic generalized metric spaces and nonlinear contractions

Mbarki A., Naciri R.

Demonstratio Mathematica

2016

Vol. 49, nr 4

437--452

We give a probabilistic generalization of the theory of generalized metric spaces [2]. Then, we prove a fixed point theorem for a self-mapping of a probabilistic generalized metric space, satisfying the very general nonlinear contraction condition without the assumption that the space is Hausdorff.

Boundary value problems for nonlinear fractional differential equations and inclusions with nonlocal and fractional integral boundary conditions

Ntouyas S. K.

Opuscula Mathematica

2013

Vol. 33, no. 1

117-138

This paper studies the boundary value problem of nonlinear fractional differential equations and inclusions of order q ∈ (1, 2] with nonlocal and integral boundary conditions. Some new existence and uniqueness results are obtained by using fixed point theorems.