The xed point result in Mustafa-Sims metrical structures obtained by Karapinar and Agarwal[Fixed Point Th. Appl., 2013, 2013:154] is deductible from a corresponding one stated in terms ofanticipative contractions over the associated (standard) metric space.

This paper deals with cocycles over ergodic metric dynamical systems with values in the semi-direct product of Z 2 and R. We show that such cocycles are recurrent under very general assumptions. Furthermore, we give criteria for the existence of invariant measures for group valued cocycles. With that, examples of continuous random dynamical systems on a compact interval without random xed point...

Results are obtained concerning the distribution of ranked relative lengths of excursions of a recurrent Markov process from a point in its state space whose inverse local time process is a stable subordinator. It is shown that for a large class of random times T the distribution of relative excursion lengths prior to T is the same as if T were a xed time. It follows that the generalized arc-si...

In this paper, we prove the existence of fixed point for J-type multi-valuedmap T in CAT(0) spaces and also we prove the strong convergence theoremsfor Ishikawa iteration scheme without using the xed point of involving map.

in this paper, we introduce a new concept of - -ϕ-contractive integral type mappings and establish some new xed point theorems in complete metric spaces.

We discuss the temporal logic`USF', involving Until, Since and the xed point operator ' of Gabbay, with semantics over the natural numbers. We show that any formula not involving Until is equivalent to one without nested xed point operators. We then prove that USF has expressive power matching that of the monadic second-order logic S1S. The proof shows that any USF-formula is equivalent to one ...

Let Q IFP be any quantiier such that FO(Q IFP), rst order logic enhanced with Q IFP and its vectorizations, equals inductive xed point logic, IFP in expressive power. It is known that for certain quantiiers Q, the equivalence FO(Q IFP) IFP is no longer true if Q is added on both sides 12, 13]. Rather, we have FO(Q IFP ; Q) < IFP(Q) in such cases. We extend these results to a great variety of qu...

Let (x n) and (^ x n) be two vector sequences converging to a common limit. First, we shall deene nonlinear hybrid procedures which consist of constructing a new vector sequence (y n) with better convergence properties than (x n) and (^ x n). Then, this procedure is used for accelerating the convergence of a given sequence and applied to the construction of xed point methods. New methods are de...

Recently, Piri and Kumam [Fixed Point Theory and Applications 2014, 2014:210] improved concept of F -contraction and proved some Wardowski and Suzuki type …xed point results in metric spaces. The aim of this article is to de…ne generalized GF -contraction and establish Wardowski and Suzuki type …xed point results in metric and ordered metric spaces and derive main results of Piri et al. as coro...

In the 1920s, algebraic topology began to develop partially due to the need for new topological techniques in solving problems in xed point theory. Indeed, the celebrated Lefschetz xed point theorem is a far reaching generalization of the well-known Brouwer xed point theorem. The eld of topological xed point theory continued to ourish through the 1940s during which much of the foundations was l...