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Aqib Saghir

Publications and source records attributed to Aqib Saghir.

4 recordsLinked to original sources
arXiv2026

A comparison of the weakest contractive conditions for Banach and Kannan mappings

We study the weakest convergence-type conditions for fixed point results for Banach and Kannan mappings. Building on Suzuki's weakest condition for Banach mappings and our previous result for Kannan mappings, we compare convergence conditions defined along Picard sequences. We give a direct proof that several weakest convergence conditions are equivalent for Kannan-type mappings on complete metric spaces. This proof is achieved without assuming the completeness or the convergence of Picard sequences; it deduces the equivalence only from the existence of fixed points. In contrast, we construct a counterexample showing that the corresponding equivalence fails for Banach contractions. Finally, we prove that this discrepancy disappears on G-complete metric spaces, clarifying the role of completeness in weakest fixed point theory.

math.FA↗
arXiv2026

On the weakest conditions for the existence of fixed points of Kannan and Chatterjea type contractions

In this paper, we study the weakest possible conditions for fixed point theorems involving two classes of mappings defined by Kannan and Chatterjea. Our approach relies on the so-called CJM condition, which was originally introduced by Ćirić [5], and later, Suzuki [18] showed that the CJM condition is necessary for the existence of fixed points and the convergence of all Picard sequences of Banach type mappings. Our aim is to extend Suzuki's approach to the case of Kannan and Chatterjea mappings. In particular, in the first case, we discuss the equivalence of previously known conditions and establish that our conditions are optimal for ensuring that all Picard sequences converge to a fixed point of a mapping.

math.FA↗
arXiv2024

Media Forensics and Deepfake Systematic Survey

Deepfake is a generative deep learning algorithm that creates or changes facial features in a very realistic way making it hard to differentiate the real from the fake features It can be used to make movies look better as well as to spread false information by imitating famous people In this paper many different ways to make a Deepfake are explained analyzed and separated categorically Using Deepfake datasets models are trained and tested for reliability through experiments Deepfakes are a type of facial manipulation that allow people to change their entire faces identities attributes and expressions The trends in the available Deepfake datasets are also discussed with a focus on how they have changed Using Deep learning a general Deepfake detection model is made Moreover the problems in making and detecting Deepfakes are also mentioned As a result of this survey it is expected that the development of new Deepfake based imaging tools will speed up in the future This survey gives indepth review of methods for manipulating images of face and various techniques to spot altered face images Four types of facial manipulation are specifically discussed which are attribute manipulation expression swap entire face synthesis and identity swap Across every manipulation category we yield information on manipulation techniques significant benchmarks for technical evaluation of counterfeit detection techniques available public databases and a summary of the outcomes of all such analyses From all of the topics in the survey we focus on the most recent development of Deepfake showing its advances and obstacles in detecting fake images

cs.CV↗