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In this paper we introduce a property and use this property to prove some common fixed point theorems in b-metric space. We also give some fixed point results on b-metric spaces endowed with an arbitrary binary relation which can be regarded as consequences of our main results. As applications, we applying our result to prove the existence of a common solution for the following system of integral equations: x (t) = ∫abK1 (t,r,x(r)) dr,x (t) = ∫abK2 (t,r,x(r)) dr, $$\matrix {x (t) = \int \limits_a^b {{K_1}} (t, r, x(r))dr, & & x(t) = \int \limits_a^b {{K_2}}(t, r, x(r))dr,} $$

In 2014, Asadi et al. introduced the concept of an M -metric space which is a generalization of a partial metric space and established Banach and Kannan fixed point theorems on M -metric spaces. In this work, we prove two fixed point theorems for Chatterjea contraction mappings in the framework of M -metric spaces. These provide partial answers to a question posed by Asadi et al. concerning a fixed point for Chatterjea contraction mappings. We also give some examples and numerical results which can be obtained from our results. [ABSTRACT FROM AUTHOR]

In this work, we introduce the concept of an s-simulation function, where s is a given real number with $$s \ge 1$$ , and use this concept for proving many results in b-metric spaces. One of these results is the existence and uniqueness of a fixed point for nonlinear mappings involving s-simulation functions. Also, we give some examples to illustrate the main results with some numerical results. Our results generalize and improve many results in b-metric spaces and also in metric spaces. [ABSTRACT FROM AUTHOR]

In this work, we introduce the new concept of a generalization of ( F , φ ) -contraction mapping and establish some existence results of φ -fixed point for such mappings. We also state some illustrative examples to support our results and give numerical experiment for approximating the φ -fixed point in this example. As an application, the obtained results are used to deduce some fixed point theorems in partial metric spaces and the application to nonlinear integral equations is given in order to illustrate the effectiveness of the main results. [ABSTRACT FROM AUTHOR]

The aim of this work is to introduce some new notions of generalized convex contraction mappings and establish some approximate fixed point theorems for such mappings in the setting of complete metric spaces. Examples and application to approximate fixed point results for cyclic mappings are also given in order to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of $(\alpha,\theta,k)$-contraction multi-valued mappings and establish some fixed point results for such mappings by using some control functions due to Jleli et al. (J. Inequal. Appl. 2014:439, 2014) in metric spaces and furnish some interesting examples to illustrate our main results. Also, we give some fixed point results in metric spaces endowed with a graph. Our results generalize and extend recent results given by some authors. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we prove some coupled coincidence point theorems for such nonlinear contraction mappings having a mixed monotone property in partially ordered metric spaces by dropping the condition of commutative. We also prove coupled common fixed point theorem for w-compatible mappings. An example of a nonlinear contraction mapping which is not applied by Lakshmikantham and Ćirić’s theorem [1] but applied by our result is given. Further, we apply our results to the existence theorem for solution of nonlinear integral equations. [Copyright &y& Elsevier]