The Meir-Keeler contraction, an important generalization of the classical Banach contraction has received enormous attention during the last four decades. In this paper, we present a review of Meir-Keeler type fixed point theorems and obtain some results using general Meir-Keeler type conditions for a sequence of maps in a metric space. Further, a recent result of Meir-Keeler type common fixed ...

In this paper, we first establish a new fixed point theorem for a Meir-Keeler type condition. As an application, we derive a simultaneous generalization of Banach contraction principle, Kannan's fixed point theorem, Chatterjea's fixed point theorem and other fixed point theorems. Some new fixed point theorems are also obtained.

In this paper we introduce a generalization of Meir-Keeler contraction forrandom mapping T : Ω×C → C, where C be a nonempty subset of a Banachspace X and (Ω,Σ) be a measurable space with being a sigma-algebra of sub-sets of. Also, we apply such type of random fixed point results to prove theexistence and unicity of a solution for an special random integral equation.

In present times, there has been a substantial endeavor to generalize the classical notion of iterated function system (IFS). We introduce new type non-linear contraction namely cyclic Meir-Keeler contraction, which is generalization famous Banach contraction. show existence and uniqueness fixed point for Using this result, we propose IFS in literature construction fractals. Furthermore, extend...

In this article, the notion of rational interpolative Meir-Keeler type contraction is discussed. The existence and uniqueness a fixed point for Das-Gupta are investigated. obtained results improve generalize existing on topic in recent literature.

In this paper, we first introduce some types of generalized $alpha$-Meir-Keeler contractions in $b$-metric-like spaces and then we establish some fixed point results for these types of contractions. Also, we present a new fixed point theorem for a Meir-Keeler contraction through rational expression. Finally, we give some examples to illustrate the usability of the obtained results.

Recently, a class of mappings named as couplings was introduced in [U.P.B. Sci. Bull. Series A, 79 (2017), 1-12]. Based on this concept, we introduce symmetric Meir-Keeler and ensure the existence strong coupled fixed points. We present some concrete examples to support obtained results. Furthermore, an application our results, investigate unique solution system integral equations.