A Generalization of a Greguš Fixed Point Theorem in Metric Spaces

We first introduce a new class of contractive mappings in the setting of metric spaces and then we present certain Greguš type fixed point theorems for such mappings. As an application, we derive certain Greguš type common fixed theorems. Our results extend Greguš fixed point theorem in metric spaces and generalize and unify some related results in the literature. An example is also given to support our main result

Fixed Points for w-Contractive Multimaps

Using the generalized Caristi's fixed point theorems we prove the existence of fixed points for self and nonself multivalued weakly w-contractive maps. Consequently, Our results either improve or generalize the corresponding fixed point results due to Latif (2007), Bae (2003), Suzuki, and Takahashi (1996) and others

Research Article Fixed Points of Multivalued Maps in Modular Function Spaces

The purpose of this paper is to study the existence of fixed points for contractive-type and nonexpansive-type multivalued maps in the setting of modular function spaces. We also discuss the concept of w-modular function and prove fixed point results for weakly-modular contractive maps in modular function spaces. These results extend several similar results proved in metric and Banach spaces settings. Copyright q 2009 M. A. Kutbi and A. Latif. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Some New Estimates for the Error of Simpson Integration Rule

We obtain some new estimates for the error of Simpson integration rule, which develop available results in the literature. Indeed, we introduce three main estimates for the residue of Simpson integration rule in L1[a,b] and L∞[a,b] spaces where the compactness of the interval [a,b] plays a crucial role

Fixed points of conditionally f-contractions in complete metric-like spaces

In this paper, we introduce the notion of a conditionally F-contraction in the setting of complete metric-like spaces and we investigate the existence of fixed points of such mappings. Our results unify, extend, and improve several results in the literature