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309 results on '"Shukla, Satish"'

8. Some generalizations of Kannan's theorems via $\sigma_c$-function

Author

Hazra, Suprokash and Shukla, Satish

Subjects
Mathematics - General Topology, 47H10, 54H25
Abstract

In this article we go on to discuss about various proper extensions of Kannan's two different fixed point theorems, introducing the new concept of $\sigma_c$-function; which is independent of the three notions of simulation function, manageable functions and R-functions. These results are the analogous to some well known theorems, and extends several known results in this literature., Comment: 18 pages

Published
2017
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13. ON GRAPHICAL FUZZY METRIC SPACES AND RELATED FIXED POINT THEOREMS.

Author

SHUKLA, SATISH, RAI, SHWETA, and MIÑANA, JUAN-JOSÉ

Subjects
*METRIC spaces, *FRACTIONAL differential equations, *TOPOLOGICAL property
Abstract

The notion of triangular inequality plays an important role in determining the structure of distance spaces. In particular, the structure of fuzzy metric spaces depends on the triangular inequality and the concerned t-norm. In most of the fixed point theorems in fuzzy metric spaces both the triangular inequality and the concerned t-norm have a major impact on the proof of fixed point theorems. Inspired by the concept of graphical metric space, it was recently introduced in N. Saleem et al., On Graphical Fuzzy Metric Spaces with Application to Fractional Differential Equations, Fractal and Fract., 6:5 (2022), 238:1-12, the notion of graphical fuzzy metric space and proved some fixed point results. The triangular inequality in such spaces is replaced by a weaker one which is directly associated with the graphical structure affine with the space. In this paper some observations on the recent results of Saleem et al. are made and so the results are revisited. Some related topological properties with some new fixed point results in graphical fuzzy metric spaces are also proved. The results of this paper generalize and extend Banach contraction principle and some other known results in this new setting. Several examples are given which support the claims and illustrate the significance of the new concepts and results. [ABSTRACT FROM AUTHOR]

Published
2024
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21. SOME FIXED POINT THEOREMS IN FUZZY METRIC-LIKE SPACES.

Author

RAI, SHWETA, DUBEY, NIKITA, and SHUKLA, SATISH

Subjects
FIXED point theory, BANACH spaces, GENERALIZATION, MATHEMATICAL mappings, MATHEMATICAL formulas
Abstract

This paper aims to establish some fixed point results for a new class of contractive type mappings in fuzzy metric-like spaces. The results of this paper generalize and extend the Banach contraction principle and some other known results in the setting of fuzzy metric-like spaces. [ABSTRACT FROM AUTHOR]

Published
2024
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22. Coincidence Point of Edelstein Type Mappings in Fuzzy Metric Spaces and Application to the Stability of Dynamic Markets

Author

Shukla, Satish, Dubey, Nikita, Shukla, Rahul, Mezník, Ivan, Shukla, Satish, Dubey, Nikita, Shukla, Rahul, and Mezník, Ivan

Abstract

In this paper, we prove a coincidence point result for a pair of mappings satisfying Edelstein-type contractive condition on fuzzy metric spaces. We describe the equilibrium of a simple demand-supply model of a dynamic market by the coincidence point of demand and supply functions. With the help of the coincidence point theorem in fuzzy metric spaces, it is showed that a dynamic market of a supply-sensitive nature (or demand-sensitive nature) always tends towards its equilibrium.

Published
2023

23. The Ittar Industry of Kannauj: A Saga of Commodification of Olfactory Aesthetics

Author

Shukla, Satish Kumar, Mukherjee, Anirban, and Middendorf, Gerad D.

Abstract

Kannauj is an historic city in northern India, which is known since antiquity for producing high quality natural ittar (natural perfume). This study explores the notion that perfume is a product of science and standardised production and marketing practices, whereas ittar is a natural product derived from traditional knowledge and craft production processes passed on through generations. The study highlights the ‘deg-bhapka’ technique of ittar production, explores the lifeworlds of the artisans, their perception of the art, discusses the main ittar varieties, and explores the role of social and cultural capital in preserving the legacy over generations. Semi-structured, open-ended interviews were used for data collection. Finally, the study examines the contemporary challenges and bottlenecks in this heritage industry and the incongruency of the art of ittar-making to the nuances of the capitalist economy. The possibilities for evolving and marketing ittar as a ‘green’, ‘organic’ and ‘indigenous’ product of traditional art and contemporary aesthetic standards are explored.

Published
2024
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32. Fixed point theorems in graphical cone metric spaces and application to a system of initial value problems.

Author

Shukla, Satish, Dubey, Nikita, and Shukla, Rahul

Subjects
*INITIAL value problems, *BANACH algebras, *CONES, *BANACH spaces, *MATHEMATICAL mappings
Abstract

In this paper, we introduce the notion of graphical cone metric spaces over Banach algebra and prove some fixed point results for a particular type of contractive mappings defined on such spaces. These results extend and generalize several results from metric, graphical metric, and cone metric spaces. Some examples that demonstrate the results proved herein are provided. An application of our results to the existence of solution of a pair of initial value problems is provided. [ABSTRACT FROM AUTHOR]

Published
2023
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