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Invariant approximation for fuzzy nonexpansive mappings

Ismat BegMujahid Abbas — 2011

Mathematica Bohemica

We establish results on invariant approximation for fuzzy nonexpansive mappings defined on fuzzy metric spaces. As an application a result on the best approximation as a fixed point in a fuzzy normed space is obtained. We also define the strictly convex fuzzy normed space and obtain a necessary condition for the set of all t -best approximations to contain a fixed point of arbitrary mappings. A result regarding the existence of an invariant point for a pair of commuting mappings on a fuzzy metric...

Fractals of generalized F− Hutchinson operator

Talat NazirSergei SilvestrovMujahid Abbas — 2016

Waves, Wavelets and Fractals

The aim of this paper is to construct a fractal with the help of a finite family of F− contraction mappings, a class of mappings more general than contraction mappings, defined on a complete metric space. Consequently, we obtain a variety of results for iterated function systems satisfying a different set of contractive conditions. Some examples are presented to support the results proved herein. Our results unify, generalize and extend various results in the existing literature.

Common fixed point results of four mappings in ordered partial metric spaces

Talat NazirSergei SilvestrovMujahid Abbas — 2016

Waves, Wavelets and Fractals

On partially ordered set equipped with a partial metric, we study the sufficient conditions for existence of common fixed points of various mappings satisfying generalized weak contractive conditions. These results unify several comparable results in the existing literature.We also study the existence of nonnegative solution of implicit nonlinear integral equation. Furthermore, we study the fractal of finite family of generalized contraction mappings defined on a partial metric space.

Existence and approximation results for SKC mappings in Busemann spaces

Safeer Hussain KhanMujahid AbbasTalat Nazir — 2017

Waves, Wavelets and Fractals

In this paper, we first discuss some properties of SKC mappings in the context of Busemann spaces and obtain a demiclosedness principle.We then prove the existence and approximation results for SKC mappings in a uniformly convex Busemann space. At the end, we give a numerical example in support of our main result. This example also shows that our iterative process is faster than some well-known iterative processes even for SKC mappings. Our results are certainly more general than many results in...

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