An algorithm for approximating a common solution of some nonlinear problems in Banach spaces with an application

In this paper, we construct a new Halpern-type subgradient extragradient iterative algorithm. The sequence generated by this algorithm converges strongly to a common solution of a variational inequality, an equilibrium problem, and a J-fixed point of a continuous J-pseudo-contractive map in a uniformly smooth and two-uniformly convex real Banach space. Also, the theorem is applied to approximate a common solution of a variational inequality, an equilibrium problem, and a convex minimization problem. Moreover, a numerical example is given to illustrate the implementability of our algorithm. Finally, the theorem proved complements, improves, and unifies some related recent results in the literature.

Existence of Solutions for Anti-Periodic Fractional Differential Inclusions Involving ψ-Riesz-Caputo Fractional Derivative

In this paper, we investigate the existence of solutions for a class of anti-periodic fractional differential inclusions with ψ -Riesz-Caputo fractional derivative. A new definition of ψ -Riesz-Caputo fractional derivative of order α is proposed. By means of Contractive map theorem and nonlinear alternative for Kakutani maps, sufficient conditions for the existence of solutions to the fractional differential inclusions are given. We present two examples to illustrate our main results.

SEPARABLY CLOSED FIELDS AND CONTRACTIVE ORE MODULES

We consider valued fields with a distinguished contractive map as valued modules over the Ore ring of difference operators. We prove quantifier elimination for separably closed valued fields with the Frobenius map, in the pure module language augmented with functions yielding components for a p-basis and a chain of subgroups indexed by the valuation group.

A fixed point theorem for generalized weak contractions

A fixed point theorem for a generalized weak contractive map in a metric space is proven by generalizing some recent results of Djoric [4, Theorem 2.2], Zhang and Song [30, Corollary 2.2] and others. The result is illustrated by examples.

A generalization of Ciric fixed point theorems

In this paper, we state and prove a generalization of Ciric fixed point theorems in metric space by using a new generalized quasi-contractive map. These theorems extend other well known fundamental metrical fixed point theorems in the literature (Banach [1], Kannan [11], Nadler [13], Reich [15], etc.) Moreover, a multi-valued version for generalized quasi-contraction is also established.

Concrete Realizations of Quotients of Operator Spaces

Let $\mathscr{B}$ be a unital C*-subalgebra of a unital C*-algebra $\mathscr{A}$, so that $\mathscr{A}/\mathscr{B}$ is an abstract operator space. We show how to realize $\mathscr{A}/\mathscr{B}$ as a concrete operator space by means of a completely contractive map from $\mathscr{A}$ into the algebra of operators on a Hilbert space, of the form $A \mapsto [Z, A]$ where $Z$ is a Hermitian unitary operator. We do not use Ruan's theorem concerning concrete realization of abstract operator spaces. Along the way we obtain corresponding results for abstract operator spaces of the form $\mathscr{A}/\mathscr{V}$ where $\mathscr{V}$ is a closed subspace of $\mathscr{A}$, and then for the more special cases in which $\mathscr{V}$ is a $*$-subspace or an operator system.

EXPLICIT DERIVATION OF RETURN MAPS FOR PLANAR VECTOR FIELDS WITH NILPOTENT LINEAR PART WITH A CENTER OR A FOCUS

For planar vector fields with nilpotent linear part with a center or a focus it is shown that, remarkably, there exist substitutions after which the equations become regular perturbations of Hamiltonian systems. The return map is then obtained as a convergent series by iterating a contractive map, yielding formulas suitable for numerical calculations and estimates for the errors.