Research Papers by Swati Antal
AIMS Mathematics, 2022
In this paper, we generate some non-classical variants of Julia and Mandelbrot sets, utilizing th... more In this paper, we generate some non-classical variants of Julia and Mandelbrot sets, utilizing the Jungck-Ishikawa fixed point iteration system equipped with s-convexity. We establish a novel escape criterion for complex polynomials of a higher degree of the form z n + az 2 − bz + c, where a, b and c are complex numbers and furnish some graphical illustrations of the generated complex fractals. In the sequel, we discuss the errors committed by the majority of researchers in developing the escape criterion utilizing distinct fixed point iterations equipped with s-convexity. We conclude the paper by examining variation in images and the impact of parameters on the deviation of dynamics, color and appearance of fractals. It is fascinating to notice that some of our fractals represent the traditional Kachhi Thread Works found in the Kutch district of Gujarat (India) which is useful in the Textile Industry.
Papers by Swati Antal
Jnanabha
In this paper we introduce the notion of a Caristi-Banach type ZbR - contraction in the framework... more In this paper we introduce the notion of a Caristi-Banach type ZbR - contraction in the framework of b-metric space endowed with a transitive relation that combine the ideas of Caristi type contraction and Banach contraction with a help of simulation function. We present an example to clarify the statement of the given result.
Mathematical Methods in the Applied Sciences
Journal of Function Spaces
In this paper, utilizing the Fibonacci-Mann iteration process, we explore Julia and Mandelbrot se... more In this paper, utilizing the Fibonacci-Mann iteration process, we explore Julia and Mandelbrot sets by establishing the escape criteria of a transcendental function, sin z n + a z + c , n ≥ 2 ; here, z is a complex variable, and a and c are complex numbers. Also, we explore the effect of involved parameters on the deviance of color, appearance, and dynamics of generated fractals. It is well known that fractal geometry portrays the complexity of numerous complicated shapes in our surroundings. In fact, fractals can illustrate shapes and surfaces which cannot be described by the traditional Euclidean geometry.
AIMS Mathematics, 2022
In this paper, we generate some non-classical variants of Julia and Mandelbrot sets, utilizing th... more In this paper, we generate some non-classical variants of Julia and Mandelbrot sets, utilizing the Jungck-Ishikawa fixed point iteration system equipped with $ s $-convexity. We establish a novel escape criterion for complex polynomials of a higher degree of the form $ z^n + az^2 -bz + c $, where $ a, \; b $ and $ c $ are complex numbers and furnish some graphical illustrations of the generated complex fractals. In the sequel, we discuss the errors committed by the majority of researchers in developing the escape criterion utilizing distinct fixed point iterations equipped with $ s $-convexity. We conclude the paper by examining variation in images and the impact of parameters on the deviation of dynamics, color and appearance of fractals. It is fascinating to notice that some of our fractals represent the traditional Kachhi Thread Works found in the Kutch district of Gujarat (India) which is useful in the Textile Industry.
The aim of this paper is to prove the existence and uniqueness of coupled coincidence best proxim... more The aim of this paper is to prove the existence and uniqueness of coupled coincidence best proximity point using proximal (Z ω)-couple contraction in partially ordered metric spaces. Results obtained in this paper extend and generalize some well known fixed point results of the literature. We provide an example in support of the results.
International Journal of Nonlinear Analysis and Applications, 2022
We introduce '{C}iri'{c} type $ mathcal{Z}_mathcal{R} $-contraction to investigate the ex... more We introduce '{C}iri'{c} type $ mathcal{Z}_mathcal{R} $-contraction to investigate the existence of single fixed point under a binary relation. In the sequel we demonstrate that variety of contractions are obtained as consequences of our contraction. Also we provide illustrative examples to demonstrate the significance of '{C}iri'{c} type $ mathcal{Z}_mathcal{R} $-contraction in the existence of fixed point for discontinuous map via binary relation. The paper is concluded by applications to solve an integral equation and a nonlinear matrix equation.
Communications of The Korean Mathematical Society, 2020
The purpose of this paper is to introduce the notion of generalized multivalued Z-contraction and... more The purpose of this paper is to introduce the notion of generalized multivalued Z-contraction and generalized multivalued Suzuki type Z-contraction for pair of mappings and establish common fixed point theorems for such mappings in complete metric spaces. Results obtained in this paper extend and generalize some well known fixed point results of the literature. We deduce some corollaries from our main result and provide examples in support of our results.
In 1922, Polish mathematician Stefan Banach [2] gave a fixed point theorem. It is also known as t... more In 1922, Polish mathematician Stefan Banach [2] gave a fixed point theorem. It is also known as the Banach Contraction mapping theorem or principle (BCP). It is an important tool in the metric fixed point theory. It confirms the existence and uniqueness of fixed point of certain self maps of metric spaces and provides a constructive method to find fixed points. There are so many extension, generalizations of BCP in different settings and there applications. Among them, In 1976, Caristi [4] proved a fixed point theorem and applied to derive a generalization of the Contraction Mapping Principle in a complete metric space. Recently, In 2019, E. Karapinar et al., [9] give a new fixed point theorem in b metric space which is inspired from both Caristi and Banach. b metric space introduced by Czerwik [5] to generalize the concept of metric space by introducing a real number s ≥ 1 in the triangle inequality of metric space. Inspired by E. Karapinar et al., [9] we introduce the notion of a ...
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2021
In the present paper, we introduce the notion of generalized F <contraction and establish some …x... more In the present paper, we introduce the notion of generalized F <contraction and establish some …xed point results for such mappings, which extend and generalize the result of Alam and Imdad [1], Sawangsup et al. [23] and many others. Our results reveal that the assumption of M-closedness of underlying binary relation is not a necessary condition for the existence of …xed points in relational metric spaces. We also derive some N-order …xed point theorems from our main results. As an application of our main result, we …nd a solution to a certain class of nonlinear matrix equations.
Dynamic Systems and Applications, 2020
Journal of Nonlinear Sciences and Applications, 2020
In this paper, we introduce the concept of generalized Suzuki type α-Z-contraction concerning a s... more In this paper, we introduce the concept of generalized Suzuki type α-Z-contraction concerning a simulation function ζ in b-metric space and prove the existence of fixed point results for this contraction. Our result extend the fixed point result of [A.
Fractal and Fractional, 2021
We explore some new variants of the Julia set by developing the escape criteria for a function si... more We explore some new variants of the Julia set by developing the escape criteria for a function sin(zn)+az+c, where a,c∈C, n≥2, and z is a complex variable, utilizing four distinct fixed point iterative methods. Furthermore, we examine the impact of parameters on the deviation of dynamics, color, and appearance of fractals. Some of these fractals represent the stunning art on glass, and Rangoli (made in different parts of India, especially during the festive season) which are useful in interior decoration. Some fractals are similar to beautiful objects found in our surroundings like flowers (to be specific Hibiscus and Catharanthus Roseus), and ants.
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Research Papers by Swati Antal
Papers by Swati Antal