In this paper, a new self-adaptive step size algorithm to approximate the solution of split minimization problem and fixed point nonexpansive mappings was constructed, which combined proximal modified Mann’s iterative method with inertial extrapolation. The strong convergence theorem provided in framework Hilbert spaces then proven under some suitable conditions. Our result improved related res...

this paper studies a fractional boundary value problem of nonlineardifferential equations of arbitrary orders. new existence and uniquenessresults are established using banach contraction principle. other existenceresults are obtained using schaefer and krasnoselskii fixed point theorems.in order to clarify our results, some illustrative examples are alsopresented.

in this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in banach spaces admitting the existence of a lower solution.