If (X, d) is a complete metric space and T : X → X is a contraction mapping, then the conclusion of the Banach-Caccioppoli contraction principle is that the sequence of successive approximations of T starting from any point of the space converges to a unique fixed point. In this paper, we obtain a sufficient and necessary condition of the above conclusion in terms of the so-called strong Leader...

The Hirsch-index is an index for measuring and comparing the output of researchers. Under the condition of monotonicity, Woeginger [7] provides a characterization of the Hirsch-index by three axioms in 2008. Replacing monotonicity by expansion consistency, we characterize the Hirsch-index by only two of Woeginger’s axioms. Besides, we also introduce an axiom contraction consistency. It is a dua...

A fixed point theorem is proved for non-self multi-valued mappings in a metrically convex complete metric space satisfying a slightly stronger contraction condition than in Rhoades [3] and under a weaker boundary condition than in Itoh [2] and Rhoades [3].

Self-similar random fractal measures were studied by Hutchinson and Rüschendorf. Working with probability metric in complete metric spaces, they need the first moment condition for the existence and uniqueness of these measures. In this paper, we use contraction method in probabilistic metric spaces to prove the existence and uniqueness of self-similar random fractal measures replacing the firs...

The purpose of this paper is to present the definition of [Formula: see text]-contractive mapping and to discuss the relation of [Formula: see text]-contractive mappings and [Formula: see text]-contractive mappings. Furthermore, the generalized [Formula: see text]-contraction mapping principle has been proved without the uniqueness condition. Meanwhile, the generalized [Formula: see text]-contr...

The aim of this article is to prove some fixed point theorems in the context of dislocated quasi metric spaces. We have established a new fixed point theorem in complete dislocated quasi metric space using some new type of rationl contraction conditions. We have also proved a unique fixed point for generalized contraction by omitting the condition of continuity imposed by C. T. Aage and J. N. S...

Researchers have identified and defined β- approach normed space if some conditions are satisfied. In this work, we show that every is a space.However, the converse not necessarily true by giving an example. addition, define β – Banach space, examples given. We also solve problems. discuss finite β-dimensional app-normed β-complete consequent app- space. explain metric but give propositions. If...

Objective Continuous and intermittent stimuli with green light affect the pupillary light response (PLR) differently. Since the majority of pupillometric studies use blue and red lights, we investigated the effect of continuous and intermittent stimulations on the PLR using red and blue lights. Methods Seventeen healthy subjects underwent continuous- and intermittent light stimuli, using red ...

in this paper, we establish and prove the existence of best proximity points for multivalued cyclic $f$- contraction mappings in complete metric spaces. our results improve and extend various results in literature.

recently, choudhury and metiya [fixed points of weak contractions in cone metric spaces, nonlinear analysis 72 (2010) 1589-1593] proved some fixed point theorems for weak contractions in cone metric spaces. weak contractions are generalizations of the banach's contraction mapping, which have been studied by several authors. in this paper, we introduce the notion of $f$-weak contractions and als...