Browsing by Author "Kumar, Anil"

Now showing 1 - 3 of 3

Citation - WoS: 10
Citation - Scopus: 10
Existence of Local and Global Solutions To Fractional Order Fuzzy Delay Differential Equation With Non-Instantaneous Impulses
(Amer inst Mathematical Sciences-aims, 2022) Malik, Muslim; Sajid, Mohammad; Baleanu, Dumitru; Kumar, Anil
The main concern of this manuscript is to examine some sufficient conditions under which the fractional order fuzzy delay differential system with the non-instantaneous impulsive condition has a unique solution. We also study the existence of a global solution for the considered system. Fuzzy set theory, Banach fixed point theorem and Non-linear functional analysis are the major tools to demonstrate our results. In last, an example is given to illustrate these analytical results.
Citation - WoS: 2
Citation - Scopus: 2
Invariant Approximation Results Via Common Fixed Point Theorems for Generalized Weak Contraction Maps
(Hindawi Ltd, 2014) Kumar, Anil; Tas, Kenan; Rathee, Savita
A common fixed point theorem for generalized (phi,phi,L)(f,g)-weak contraction in a metric space is established. As an application, some common fixed point results in normed linear spaces are obtained. We also study some results on best approximation via common fixed point theorems. Our result improves some results from the existing literature. Some illustrative examples to highlight the realized improvements are also furnished.
Citation - WoS: 4
Citation - Scopus: 4
Note on Common Fixed Point Theorems in Convex Metric Spaces
(Mdpi, 2021) Kumar, Anil; Tas, Aysegul
In the present paper, we pointed out that there is a gap in the proof of the main result of Rouzkard et al. (The Bulletin of the Belgian Mathematical Society 2012). Then after, utilizing the concept of (E.A.) property in convex metric space, we obtained an alternative and correct version of this result. Finally, it is clarified that in the theory of common fixed point, the notion of (E.A.) property in the set up of convex metric space develops some new dimensions in comparison to the hypothesis that a range set of one map is contained in the range set of another map.