* Correspondence: ming@mail. nhcue.edu.tw Department of Applied Mathematics, National Hsinchu University of Education, Hsin-Chu, Taiwan Full list of author information is available at the end of the article Abstract In this article, we introduce the notions of (j φ)-weak contraction mappings and (ψ φ)-weak contraction mappings in complete generalized metric spaces and prove two theorems which a...

We correct the proof of Theorem 6 in the letter ‘‘Fixed point theory for cyclic weak φ-contraction’’ [E. Karapınar, Fixed point theory for cyclic weak φ-contraction, Appl. Math. Lett. 24 (6) (2011) 822–825]. © 2010 Elsevier Ltd. All rights reserved.

jachymski [ proc. amer. math. soc., 136 (2008), 1359-1373] gave modified version of a banach fixed point theorem on a metric space endowed with a graph. in the present paper, (g, φ)-graphic contractions have been de ned by using a comparison function and studied the existence of fixed points. also, hardy-rogers g-contraction have been introduced and some fixed point theorems have been proved. s...

LetX be a Banach space with dualX∗, and letK be a nonempty subset ofX. A gauge function is a continuous strictly increasing function φ : R → R such that φ 0 0 and limt→∞φ t ∞. The duality mapping Jφ : X → X∗ associated with a gauge function φ is defined by Jφ x : {f ∈ X∗ : 〈x, f〉 ‖x‖‖f‖, ‖f‖ φ ‖x‖ }, x ∈ X, where 〈·, ·〉 denotes the generalized duality pairing. In the particular case φ t t, the ...

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...

In this paper, we introduce the notion of weak $psi$-quasi contraction in generalized metric spaces and using this notion we obtain conditions for the existence of fixed points of a self map in $D$-complete generalized metric spaces. We deduce some corollaries from our result and provide examples in support of our main result.

Cyclic weak φ-contraction mapping is introduced in Menger space and fixed point theorem for such mappings are studied in Menger space. Mathematics Subject Classification 47H10, 54H25