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The aim of this work is to modify the notions of α-admissible and α-ψ-contractive mappings and establish new fixed point theorems for such mappings in complete metric spaces. Presented theorems provide main results of Karapinar and Samet (Abstr. Appl. Anal. 2012Anal. :793486, 2012 and Samet et al. (Nonlinear Anal. 75:2154-2165 as direct corollaries. Moreover, some examples and applications to integral equations are given here to illustrate the usability of the obtained results.

We first introduce the concept of b-metric-like space which generalizes the notions of partial metric space, metric-like space and b-metric space. Then we establish the existence and uniqueness of fixed points in a b-metric-like space as well as in a partially ordered b-metric-like space. As an application, we derive some new fixed point and coupled fixed point results in partial metric spaces, metric-like spaces and b-metric spaces. Moreover, some examples and an application to integral equations are provided to illustrate the usability of the obtained results. MSC: Primary 47H10; 54H25; 55M20

We present some new common fixed point theorems for a pair of nonlinear mappings defined on an ordered Banach space. Our results extend several earlier works. An application is given to show the usefulness and the applicability of the obtained results.

The aim of this paper is to introduce new concepts ofα-η-complete metric space andα-η-continuous function and establish fixed point results for modifiedα-η-ψ-rational contraction mappings inα-η-complete metric spaces. As an application, we derive some Suzuki type fixed point theorems and new fixed point theorems forψ-graphic-rational contractions. Moreover, some examples and an application to integral equations are given here to illustrate the usability of the obtained results.

Suzuki's fixed point results from (Suzuki, Proc. Am. Math. Soc. 136:1861Soc. 136: -1869Soc. 136: , 2008 and (Suzuki, Nonlinear Anal. 71:5313-5317, 2009) are extended to the case of metric type spaces and cone metric type spaces. Examples are given to distinguish our results from the known ones. MSC: 47H10; 54H25

We first introduce a new concept of b-dislocated metric space as a generalization of dislocated metric space and analyze different properties of such spaces. A fundamental result for the convergence of sequences in b-dislocated metric spaces is established and is employed to prove some common fixed point results for four mappings satisfying the generalized weak contractive condition in partially ordered b-dislocated metric spaces. Moreover, some examples and applications to integral equations are given here to illustrate the usability of the obtained results.

We discuss the existence of fixed points of asymptotic pointwise mappings in metric spaces. This is the nonlinear version of some known results proved in Banach spaces. We also discuss the case of multivalued mappings.MSC: Primary 47H09; Secondary 47H10.