Sehgal–Guseman-Type Fixed Point Theorem in b-Rectangular Metric Spaces

In this paper, we prove a Sehgal–Guseman-type fixed point theorem in b-rectangular metric spaces which provides a complete solution to an open problem raised by Zoran D. Mitrović (A note on a Banach’s fixed point theorem in b-rectangular metric space and b-metric space). The result presented in the paper generalizes and unifies some results in fixed point theory.

Fuzzy Triple Controlled Metric Spaces and Related Fixed Point Results

In this study, we introduce fuzzy triple controlled metric space that generalizes certain fuzzy metric spaces, like fuzzy rectangular metric space, fuzzy rectangular b -metric space, fuzzy b -metric space, and extended fuzzy b -metric space. We use f , g , h , three noncomparable functions as follows: m q μ , η , t + s + w ≥ m q μ , ν , t / f μ , ν ∗ m q ν , ξ , s / g ν , ξ ∗ m q ξ , η , w / h ξ , η . We prove Banach fixed point theorem in the settings of fuzzy triple controlled metric space that generalizes Banach fixed point theorem for aforementioned spaces. An example is presented to support our main results. We also apply our technique to the uniqueness for the solution of an integral equation.

Fixed Point Theorems on Generalized Rectangular Metric Spaces

In this paper, we introduce the notion of generalized rectangular metric spaces which extends rectangular metric spaces introduced by Branciari. Analogues of the some well-known fixed point theorems are proved in this space. With an example, it is shown that a generalized rectangular metric space is neither a G-metric space nor a rectangular metric space. Our results generalize many known results in fixed point theory.

Fixed Point of Interpolative Rus–Reich–Ćirić Contraction Mapping on Rectangular Quasi-Partial b-Metric Space

The purpose of this study is to introduce a new type of extended metric space, i.e., the rectangular quasi-partial b-metric space, which means a relaxation of the symmetry requirement of metric spaces, by including a real number s in the definition of the rectangular metric space defined by Branciari. Here, we obtain a fixed point theorem for interpolative Rus–Reich–Ćirić contraction mappings in the realm of rectangular quasi-partial b-metric spaces. Furthermore, an example is also illustrated to present the applicability of our result.

PARTIAL b_{v}(s), PARTIAL v-GENERALIZED AND b_{v}(θ) METRIC SPACES AND RELATED FIXED POINT THEOREMS

In this paper, we have introduced three new generalized metric spaces called partial $b_{v}\left( s\right) $, partial $v$-generalized and $b_{v}\left(\theta \right) $ metric spaces which extend $b_{v}\left( s\right) $ metricspace, $b$-metric space, rectangular metric space, $v$-generalized metricspace, partial metric space, partial $b$-metric space, partial rectangular $%b $-metric space and so on. We have proved some famous theorems such as Banach, Kannan and Reich fixed point theorems in these spaces. Also, we have given somenumerical examples to support our definitions. Our results generalize several corresponding results in literature.

Fixed Point Problems in Cone Rectangular Metric Spaces with Applications

In this paper, we introduce an ordered implicit relation and investigate some new fixed point theorems in a cone rectangular metric space subject to this relation. Some examples are presented as illustrations. We obtain a homotopy result as an application. Our results generalize and extend several fixed point results in literature.

Some new fixed point results in rectangular metric spaces with an application to fractional-order functional differential equations

In this paper, we establish some new fixed point theorems for generalized ϕ–ψ-contractive mappings satisfying an admissibility-type condition in a Hausdorff rectangular metric space with the help of C-functions. In this process, we rectify the proof of Theorem 3.2 due to Budhia et al. [New fixed point results in rectangular metric space and application to fractional calculus, Tbil. Math. J., 10(1):91–104, 2017]. Some examples are given to illustrate the theorems. Finally, we apply our result (Corollary 3.6) to establish the existence of a solution for an initial value problem of a fractional-order functional differential equation with infinite delay.

A note on a Banach’s fixed point theorem in b-rectangular metric space and b-metric space

In this note we give very short proofs for Banach contraction principle theorem in the b-rectangular metric spaces and b-metric spaces. Our result provides a complete solution to an open problem raised by George, Radenović, Reshma and Shukla.