arXiv subjects
Publications and source records attributed to T. Bag.
Following the definition of perturbed metric space, in this paper, some fixed point theorems are established for $ F $-perturbed mappings in complete perturbed metric spaces and justify the result by counter example. Finally, an application of this theorem for the existence of a solution for the second-order boundary value problem is given.
The objective of this manuscript is to introduce and develop the concept of a generalized $θ$-parametric metric space-a novel extension that enriches the modern metric fixed point theory. We study of its fundamental properties, including convergence and Cauchy sequences that establishes a solid theoretical foundation. A significant highlight of our work is the formulation of Suzuki-type fixed point theorem within this framework which extends classical results in a meaningful way. To demonstrate the depth and applicability of our findings, we construct non-trivial examples that illustrate the behavior of key concepts. Moreover, as a practical application, we apply our main theorem to analyze an economic growth model, demonstrating its utility in solving fractional differential equations that arise in dynamic economic systems.
This article explores several fundamental aspects of fuzzy $\mathscr{F}$-metric spaces and their applications in mathematical analysis. We investigate some essential properties concerning compactness and total boundedness in fuzzy $\mathscr{F}$-metric spaces. Within this framework, we present a fixed point theorem and demonstrate its utility by applying it to the satellite web coupling problem. To support the theoretical findings, illustrative examples and a graphical representation of the contraction condition are also provided.
The objective of this work is the construction of `Boyd-Wong fixed point theorem' in the setting of generalized parametric metric space and discussion its application on existence criteria of solutions to a second order initial value problem. Also an analogue of `Banach type fixed point theorem of generalized parametric metric space is proved and its application on the existence of a solution of first order periodic boundary value differential equation is examined.
In this paper, ideas of open ball, closed ball, compact set are introduced and some related basic properties are studied. Some topological properties and some other well known results of metric spaces including Cantor intersection theorem are established in generalized parametric metric space setting.
S-metric and b-metric spaces are metrizable, but it is still quite impossible to get an explicit form of the concerned metric function. To overcome this, the notion of $ϕ$-metric is developed by making a suitable modification in triangle inequality and its properties are pretty similar to metric function. It is shown that one can easily construct a $ϕ$-metric from existing generalized distance functions like S-metric, b-metric, etc. and those are $ϕ$-metrizable. The convergence of sequence on those metric spaces is identical to the respective induced $ϕ$-metric spaces. So, unlike metrics, concerned $ϕ$-metric can be easily constructed and $ϕ$-metric functions may play the role of metric functions substantially. Also, the structure of $ϕ$-metric spaces is studied and some fixed point theorems are established.
In this paper, concept of fuzzy continuous operator, fuzzy bounded linear operator are introduced in fuzzy strong $ϕ$-b-normed linear spaces and their relations are studied. Idea of operator fuzzy norm is developed and completeness of BF(X,Y) is established.
In this paper, definition of fuzzy strong $ϕ$-b-normed linear space is given. Here the scalar function |c| is replaced by a general function $ϕ$(c) where ϕ satisfies some properties. Some basic results on finite dimensional fuzzy strong $ϕ$-b-normed linear space are studied.