We study Krasnoselskii-Mann style iterative algorithms for approximating fixpoints of asymptotically weakly contractive mappings, with a focus on providing generalized convergence proofs along explicit rates convergence. More specifically, we define new notion being ψ-weakly modulus, and present series abstract theorems which both generalize unify known results from the literature. Rates are fo...

In this paper, we study for some of the fixed point of mapping for a self map on a metric space under a contractive of integral type.

This article investigates some properties of quasi-cyclic and cyclic Jungck modified TS-iterative schemes in complete metric spaces and Banach spaces. In particular, properties of convergence of distances and sequences associated with the self-mappings which define the Jungck modified TS-iterative procedures are studied as well as some properties concerning the convergence of the solution to co...

In this paper, we introduce a modified Mann iterative process for strictly pseudo-contractive mappings and obtain a strong convergence theorem in the framework of q-uniformly smooth Banach spaces. Our results improve and extend the recent ones announced by (Kim and Xu 2005), (Xu 2004) and some others.

‎In this paper‎, ‎we introduce the concept of Su-type contractive mapping and establish fixed point theorems for such mappings in the setting of ordered‎ ‎extended partial $b$-metric space‎. ‎We also develop an‎ ‎application for Fredholm type integral equations to‎ ‎validate our main result and a non-trivial example is given to‎ ‎elucidate our work.

Very recently, Agarwal et al. (Fixed Point Theory Appl. 2012:40, 2012) initiated the study of fixed point theorems for mappings satisfying cyclical generalized contractive conditions in complete partial metric spaces. In the present paper, we study some fixed point theorems for a mapping satisfying a cyclical generalized contractive condition based on a pair of altering distance functions in co...

We introduce a modified Noor iteration scheme generated by an infinite family of strict pseudo-contractive mappings and prove the strong convergence theorems of the scheme in the framework of q−uniformly smooth and strictly convex Banach space. Results shown here are extensions and refinements of previously known results.

Fixed point results for a self-map satisfying locally contractive conditions on a closed ball in an ordered 0-complete quasi-partial metric space have been established. Instead of monotone mapping, the notion of dominated mappings is applied. We have used weaker metric, weaker contractive conditions, and weaker restrictions to obtain unique fixed points. An example is given which shows that how...

The aim of this paper is to prove a convergence theorem of a generalized Ishikawa iteration sequence for two multivalued strongly pseudo-contractive mappings by using an approximation method in real uniformly smooth Banach spaces. We generalize and extend the results of Chang and Chang, Cho, Lee, Jung, and Kang.

It is well known that the classical contraction mapping principle of Banach is a fundamental result in fixed point theory. Several authors have obtained various extensions and generalizations of Banach’s theorems by considering contractive mappings on different metric spaces. Huang and Zhang [1] have replaced real numbers by ordering Banach space and have defined a cone metric space. They have ...