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.

The purpose of this work is to consider an initial value problem for neutral functional diierential equations with state dependent and vanishing delays. A gener-alised version of Schauder's xed point theorem which is based on the ball measure of noncompactness is used to obtain local existence of solutions and a comparison theorem. Results on continuation, uniqueness and continuous dependence o...

We shall show that a recent version of Ekeland's principle in F-type topological spaces due to Fang from 1996 is implied by the Brezis-Browder principle on ordered sets. We give a series of equivalent formulations of Ekeland's principle in F-type topo-logical spaces, i.e. Penot's ower petal theorem, Takahashi's minimization principle and two theorems due to Oettli and Th era and show the equiva...

Existence of fixed point in orthogonal metric spaces has been initiated recently by Eshaghi and et al. [On orthogonal sets and Banach fixed Point theorem, Fixed Point Theory, in press]. In this paper, we introduce the notion of the strongly orthogonal sets and prove a genuine generalization of Banach' fixed point theorem and Walter's theorem. Also, we give an example showing that our main theor...

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...

In this paper, we first establish a new fixed point theorem for a Meir-Keeler type condition. As an application, we derive a simultaneous generalization of Banach contraction principle, Kannan's fixed point theorem, Chatterjea's fixed point theorem and other fixed point theorems. Some new fixed point theorems are also obtained.

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 this paper, stochastic generalizations of some fixed point for operators satisfying random contractively generalized hybrid and some other contractive condition have been proved. we discuss also the existence of a solution to a nonlinear random integral equation in banah spaces.