In the present paper, we refine the notion of the partial modular metric defined by Hosseinzadeh and Parvaneh to eliminate the occurrence of discrepancies in the non-zero self-distance and triangular inequality. In support of this, we discuss non-trivial examples. Finally, we prove a common fixed-point theorem for four self-mappings in partial modular metric space and an application to our result; the existence of a solution for a system of Volterra integral equations is discussed.

For two real Banach algebras $\mathbb{A}_1$ and $\mathbb{A}_2$, let $K_p$ be the projective cone in $\mathbb{A}_1\otimes_\gamma \mathbb{A}_2$. Using this we define a cone norm on the algebraic tensor product of two vector spaces over the Banach algebra $\mathbb{A}_1\otimes_\gamma \mathbb{A}_2$ and discuss some properties. We derive some fixed point theorems in this projective cone normed tensor product space over Banach algebra with a suitable example. For two self mappings $S$ and $T$ on a cone Banach space over Banach algebra, the stability of the iteration scheme $x_{2n+1}=Sx_{2n}$, $x_{2n+2}=Tx_{2n+1},\;n=0,1,2,...$ converging to the common fixed point of $S$ and $T$ is also discussed here.

In the present paper, we introduce the notion of $C^{*}$-algebra-valued partial modular metric space satisfying the symmetry property that generalizes partial modular metric space, $C^{*}$-algebra-valued partial metric space, and $C^{*}$-algebra-valued modular metric space and discuss it with examples. Some fixed point results using $(\varphi ,\mathcal{MF})$-contraction mapping are discussed in such space. In addition, we study the stability of obtained results in the spirit of Ulam and Hyers. As an application, we also provide the existence and uniqueness of the solution for a system of Fredholm integral equations.

This article introduces a new type of $C^{*}$-algebra valued modular G-metric spaces that is more general than both $C^{*}$-algebra valued modular metric spaces and modular G-metric spaces. Some properties are also discussed with examples. A few common fixed point results in $C^{*}$-algebra valued modular G-metric spaces are discussed using the “$C_{*}$-class function”, along with some suitable examples to validate the results. Ulam–Hyers stability is used to check the stability of some fixed point results. As applications, the existence and uniqueness of solutions for a particular problem in dynamical programming and a system of nonlinear integral equations are provided.

The concept of G-Class (generalized C-class type) function is introduced in this study. By introducing a new contractive condition via a G-class function, some fixed point findings for partially weakly increasing mappings are introduced in ordered dualistic partial metric spaces. In support of these results, some valid examples are given.

Comments and Suggestions for Authors: Author introduced the notion of generalized _N_-metric spaces (gNms) derived from the idea of path integrals with examples and diverse situations. Author may consider the following points: * Based on the thi...