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In this paper we introduce the notion of modified w -distance ( mw -distance) on a quasi-metric space which generalizes the concept of quasi-metric. We obtain a fixed point theorem for generalized contractions with respect to mw -distances on complete quasi-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper we present some important generalizations of the Banach contraction principle in which the Lipschitz constant k is replaced by some real-valued control function. For the applications to the fractal, we obtain the fixed point theorem of the some generalized contraction in the fractal space. [ABSTRACT FROM AUTHOR]

Abstract: In this work, we study some new common fixed point results for generalized contractive multi-valued non-self-mappings on complete metric spaces. [Copyright &y& Elsevier]

Abstract: We obtain two fixed point theorems for complete partial metric space that, by one hand, clarify and improve some results that have been recently published in Topology and its Applications, and, on the other hand, generalize in several directions the celebrated Boyd and Wong fixed point theorem and Matkowski fixed point theorem, respectively. [Copyright &y& Elsevier]

Abstract: We establish a geometric lemma giving a list of equivalent conditions for some subsets of the plane. As its application, we get that various contractive conditions using the so-called altering distance functions coincide with classical ones. We consider several classes of mappings both on metric spaces and ordered metric spaces. In particular, we show that unexpectedly, some very recent fixed point theorems for generalized contractions on ordered metric spaces obtained by Harjani and Sadarangani [J. Harjani, K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal. 72 (2010) 1188–1197], and Amini-Harandi and Emami [A. Amini-Harandi, H. Emami A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Anal. 72 (2010) 2238–2242] do follow from an earlier result of O’Regan and Petruşel [D. O’Regan and A. Petruşel, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl. 341 (2008) 1241–1252]. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to extend a very recent result proved by Dorić (2009) , as well as other theorems given by Rhoades (2001) and Dutta and Choudhury (2008) . [ABSTRACT FROM AUTHOR]

Abstract: In the present paper, we give some fixed point theorems for generalized contractive type mappings on partial metric space. Also, a homotopy result is given. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we introduce the class of generalized -weak contractive mappings. We establish that these mappings necessarily have a unique common fixed point in complete metric spaces. This result generalizes an existing result in metric spaces. [Copyright &y& Elsevier]

Abstract: This paper deals with the existence of hybrid fixed points involving two multivalued operators in a complete metric space. Our claim is also illustrated with applications to a class of integral inclusions for proving the existence results. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to discuss some basic problems (data dependence, well-posedness, nonself operators, homotopy results, generalized contractions) of the fixed point theory for a new type contractive multivalued operator. The results complement and extend some very recent results proved by M. Kikkawa and T. Suzuki, as well as, other theorems given by M. Frigon and A. Granas, S. Reich, I.A. Rus, etc. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to discuss some basic problems of the fixed point theory for non-self (single-valued and multivalued) generalized contractions. As consequences, new open operator principles and domain invariance theorems are obtained. The results complement and extend some known results in the literature. [Copyright &y& Elsevier]

• A fixed point result on complete partial metric space has been extended to a bivariate function. • Utilizing the partial Hausdorff metric a generalized countable partial iterated function system (GCPIFS) having generalized contractions has been formulated. • The attractor of this GCPIFS is found with the aid of HB theory. The primary interest of this article is to extend the fixed point result proved for a complete partial metric space (simply, pms) with a generalized contraction to a bivariate case. Taking this as a basic note, a generalized countable partial iterated function system (GCPIFS , for short) is introduced with the generalized contractions, using the partial Hausdorff metric. The attractor of this GCPIFS is proved as the fixed point of the generalized Hutchinson operator concentrated on the complete metric space (C B p m ⁎ (P ⁎) × C B p m ⁎ (P ⁎) , H p m ⁎ ). A certain number of examples are given to show the existence of the theoretical results which we proved. [ABSTRACT FROM AUTHOR]

Abstract: We correct the proof of Theorem 1 in the paper in the title. [Copyright &y& Elsevier]