In this paper we prove strong convergence theorems for approximating the fixed point of Lipschitzian semigroup and infinite family of nonexpansive mappings with respect to finite family of sequence {μi,n} ∞ i=1,n=1 of left strong regular invariant means and Meir-Keeler type contraction in uniformly convex and smooth Banach spaces. Our result extend and improve many recent results.

Motivated by the open question posed H. K. XU in [39] (Question 2:8), Belhadj, Ben Amar and Boumaiza introduced [5] concept of Meir-Keeler condensing operator for self-mappings a Banach space via an arbitrary measure weak noncompactness. In this paper, we introduce Meir- Keeler nonself-mappings noncompactness establish fixed point results under condition Leray-Schauder type. Some basic hybrid t...

recently, choudhury and metiya [fixed points of weak contractions in cone metric spaces, nonlinear analysis 72 (2010) 1589-1593] proved some fixed point theorems for weak contractions in cone metric spaces. weak contractions are generalizations of the banach's contraction mapping, which have been studied by several authors. in this paper, we introduce the notion of $f$-weak contractions and als...

<p>A Meir-Keeler type fixed point theorem for a family of mappings is proved in Menger probabilistic metric space (Menger PM-space). We establish that completeness the equivalent to property larger class includes continuous as well discontinuous mappings. In addition it, satisfying (ϵ - δ) non-expansive established.</p>

We introduce the notions of the asymptotic SMK-sequence with respect to the stronger MeirKeeler cone-type mapping ξ : int P ∪ {θ} → 0, 1 and the asymptotic WMK-sequence with respect to the weaker Meir-Keeler cone-type mapping φ : int P ∪ {θ} → int P ∪ {θ} and prove some common fixed point theorems for these two asymptotic sequences in cone metric spaces with regular cone P . Our results general...

Our aim in this paper is to study the existence of solution sets and its topological structure for non-localfractional differential equations on half-line a Banach space using Riemann-Liouville definition. Themain result based Meir-Keeler fixed point theorem condensing operators combined with measure ofnon-compactness. An example given illustrate feasibility our main result.

In this article to prove existence of solution of infinite system of nonlinear integral equations, we consider the space of solution containing all convergence sequences with a finite limit, as with a suitable norm is a Banach space. By creating a generalization of Meir-Keeler condensing operators which is named as F-generalized Meir-Keeler condensing operators and measure of noncompactness, we...