Ankush Chanda

Bio: Ankush Chanda is an academic researcher from VIT University. The author has contributed to research in topics: Metric space & Fixed point. The author has an hindex of 5, co-authored 21 publications receiving 78 citations. Previous affiliations of Ankush Chanda include National Institute of Technology, Durgapur.

Simulation functions: a survey of recent results

Abstract: This article surveys many of the recent works regarding simulation functions and $$\mathcal {Z}$$ -contractions that came into existence after the publication of Khojasteh et al. (Filomat 29(6):1189–1194, 2015). These results assess inclusive of simulation functions, $$\mathcal {Z}$$ -contractions, b-simulation functions, Suzuki-type $$\mathcal {Z}$$ -contractions, Darbo’s fixed point theorem, $$\alpha $$ -admissible $$\mathcal {Z}$$ -contractions, first-order periodic problems and variational inequality problems. Additionally, we consider many of the metric frameworks that have been taken into account while exploring the results.

New fixed point results in orthogonal metric spaces with an application

Abstract: In this manuscript, owing to the concept of w-distance, we prove the much acclaimed Banach's fixed point theorem in orthogonal metric spaces. Further, our paper includes a couple of illustrative examples which exhibit the purpose for such inquests. In fact, the obtained results extend and improve certain comparable results of existing literature. Eventually, our findings allow us to obtain the existence and uniqueness of solutions of nonlinear fractional differential equations associated with the Caputo fractional derivative.

Simulation functions and geraghty type results

Abstract: We concern this manuscript with Geraghty type contraction mappings via simulation functions and pull down some sufficient conditions for the existence and uniqueness of point of coincidence for several classes of mappings involving Geraghty functions in the setting of metric spaces. These findings touch up many of the existing results in the literature. Additionally, we elicit one of our main results by a non-trivial example and pose an interesting open problem for the enthusiastic readers.

Fixed point results on θ-metric spaces via simulation functions

Abstract: In a recent article, Khojasteh et al. introduced a new class of simulation functions, Z-contractions, with blending over known contractive conditions in the literature. Subsequently, in this paper, we extend and generalize the results in θ-metric context and we discuss some fixed point results in connection with existing ones. Also, we originate the notion of modified Z-contractions and explore the existence and uniqueness of fixed points of such functions on the said spaces. Finally we include examples to instantiate our main results.

Some interesting results on F-metric spaces

Abstract: In this manuscript, we prove that the newly introduced F-metric spaces are Hausdorff and first countable. We investigate some interrelations among the Lindel?fness, separability and second countability axiom in the setting of F-metric spaces. Moreover, we acquire some interesting fixed point results concerning altering distance functions for contractive type mappings and Kannan type contractive mappings in this exciting context. In addition, most of the findings are well-furnished by several non-trivial examples. Finally, we raise an open problem regarding the structure of an open set in this setting.

مستطيلة-ب متري المساحات ومبادئ الانكماش / Rectangular b-metric spaces and contraction principles

Abstract: The concept of rectangular b-metric space is introduced as a generalization of metric space, rectangular metric space and b-metric space. An analogue of Banach contraction principle and Kannan's xed point theorem is proved in this space. Our result generalizes many known results in xed point theory.

On Positive Solutions for a Fractional Thermostat Model with a Convex–Concave Source Term via $$\psi $$ψ-Caputo Fractional Derivative

Abstract: We consider a fractional thermostat model involving $$\psi $$-Caputo fractional derivatives. Two cases are discussed: the case when the source term is concave and the case when the source term is convex. For each case, the existence and uniqueness of positive solutions are investigated. Moreover, an iterative algorithm is provided to approximate the solutions. Our approach is based on a fixed point theorem on cones.

Simulation functions: a survey of recent results

Abstract: This article surveys many of the recent works regarding simulation functions and $$\mathcal {Z}$$ -contractions that came into existence after the publication of Khojasteh et al. (Filomat 29(6):1189–1194, 2015). These results assess inclusive of simulation functions, $$\mathcal {Z}$$ -contractions, b-simulation functions, Suzuki-type $$\mathcal {Z}$$ -contractions, Darbo’s fixed point theorem, $$\alpha $$ -admissible $$\mathcal {Z}$$ -contractions, first-order periodic problems and variational inequality problems. Additionally, we consider many of the metric frameworks that have been taken into account while exploring the results.

Fixed-disc results via simulation functions

Abstract: In this paper, our aim is to obtain new fixed-disc results on metric spaces. To do this, we present a new approach using the set of simulation functions and some known fixed-point techniques. We do not need to have some strong conditions such as completeness or compactness of the metric space or continuity of the self-mapping in our results. Taking only one geometric condition, we ensure the existence of a fixed disc of a new type contractive mapping.

On the qualitative analysis of the fractional boundary value problem describing thermostat control model via ψ-Hilfer fractional operator

Abstract: In this research study, we are concerned with the existence and stability of solutions of a boundary value problem (BVP) of the fractional thermostat control model with ψ-Hilfer fractional operator. We verify the uniqueness criterion via the Banach fixed-point principle and establish the existence by using the Schaefer and Krasnoselskii fixed-point results. Moreover, we apply the arguments related to the nonlinear functional analysis to discuss various types of stability in the format of Ulam. Finally, by several examples we demonstrate applications of the main findings.