Papers by Kamran Alam Khan
Arxiv, 2021
Mustafa and Sims [12] introduced the notion of G-metric as a possible generalization of usual not... more Mustafa and Sims [12] introduced the notion of G-metric as a possible generalization of usual notion of a metric space. The author generalized the notion of G-metric to more than three variables and introduced the concept of Generalized n-metric spaces [10]. In this paper, We prove Banach fixed point theorem and a Suzuki-type fixed point theorem in Generalized n-metric spaces. We also discuss applications to certain functional equations arising in dynamic programming.
Impulsive noise is a problem encountered during the acquisition and transmission of digital image... more Impulsive noise is a problem encountered during the acquisition and transmission of digital images. Fuzzy metrics dealing nicely with the nonlinear nature of digital images are used in vector median-based filters for noise reduction in colour and multichannel images. In this paper, We generalize the concept of Fuzzy metric space (In the sense of George and Veeramani) and introduce the notion of Generalized Fuzzy n-Metric Space. The theory for such spaces is developed and as practical application, we propose some new filters based on these Generalized fuzzy metrics for colour image processing.
Journal of Nonlinear and Convex Analysis, Oct 29, 2014
"Gahler ([3] ,[4]) introduced the concept of 2-metric as a possible
generalization of usual not... more "Gahler ([3] ,[4]) introduced the concept of 2-metric as a possible
generalization of usual notion of a metric space. In many cases the results obtained in the usual metric spaces and 2-metric spaces are found to be unrelated (see [5]). Mustafa and Sims [8] took a different approach and introduced the notion of G-metric. The author [6] generalized the notion of G-metric to more than three variables and introduced the concept of K-metric as a function
K: X^n---->R^+, (n> or = 3). In this paper, We improve the definition of K-metric by making symmetry condition more general. This improved metric denoted by G_n is called the Generalized n-metric. We develop the theory for generalized n-metric spaces and obtain some fixed point theorems."
Gähler ([4], [5]) introduced and investigated the notion of 2-metric spaces and 2-normed spaces ... more Gähler ([4], [5]) introduced and investigated the notion of 2-metric spaces and 2-normed spaces in sixties. These concepts are inspired by the notion of area in two dimensional Euclidean space. In this paper, we choose a fundamentally different approach and introduce a possible generalization of usual norm retaining the distance analogue properties. This generalized norm will be called as G-norm. We show that every G-normed space is a G-metric space and therefore, a topological space and develop the theory for G-normed spaces. We also introduce G-Banach spaces and obtain some fixed point theorems
The notion of a bitopological space as a triple (X,I_1,I_2), where X is a set and I_1and I_2are t... more The notion of a bitopological space as a triple (X,I_1,I_2), where X is a set and I_1and I_2are topologies on X, was first formulated by J.C.Kelly [5]. In this paper our aim is to introduce and study the notion of an N-topological space (X,I_1,I_2,………I_N). We first generalize the notion of an ordinary metric to n variables. This metric will be called K-metric. Then the notion of a quasi-pseudo-K-metric will be introduced. We then follow the approach of Kelly to introduce and study the notion of an N-topological space. An example for such a space is produced using chain topology. And finally we define and study some of the possible separation properties for N-topological spaces.
In 1994, F. J. Craveiro de carvalho and D’Azevedo Breda took up the task of generalizing the Sier... more In 1994, F. J. Craveiro de carvalho and D’Azevedo Breda took up the task of generalizing the Sierpiński space and introduced the concept of locally Sierpiński space ([4]). In this paper, we choose a different approach and propose a generalization of Sierpiński space by defining a topology analogous to Sierpiński topology with nested open sets on any arbitrary non-empty set. We then introduce the notion of Special finite generalized Sierpiński space as a special case of generalized Sierpiński space. We investigate some of the properties of the generalized Sierpiński spaces and obtained a formula for the number of finite generalized Sierpiński topologies using Stirling number of the second kind. Finally we show that every special finite generalized Sierpiński space is a D-space.
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Papers by Kamran Alam Khan
generalization of usual notion of a metric space. In many cases the results obtained in the usual metric spaces and 2-metric spaces are found to be unrelated (see [5]). Mustafa and Sims [8] took a different approach and introduced the notion of G-metric. The author [6] generalized the notion of G-metric to more than three variables and introduced the concept of K-metric as a function
K: X^n---->R^+, (n> or = 3). In this paper, We improve the definition of K-metric by making symmetry condition more general. This improved metric denoted by G_n is called the Generalized n-metric. We develop the theory for generalized n-metric spaces and obtain some fixed point theorems."
generalization of usual notion of a metric space. In many cases the results obtained in the usual metric spaces and 2-metric spaces are found to be unrelated (see [5]). Mustafa and Sims [8] took a different approach and introduced the notion of G-metric. The author [6] generalized the notion of G-metric to more than three variables and introduced the concept of K-metric as a function
K: X^n---->R^+, (n> or = 3). In this paper, We improve the definition of K-metric by making symmetry condition more general. This improved metric denoted by G_n is called the Generalized n-metric. We develop the theory for generalized n-metric spaces and obtain some fixed point theorems."